Same pattern as Angles on a line — two equal ones and 62°. New numbers, new
story. Try each one on paper, then check the working below — or watch it drawn out, the
same way the problem above is.
Question 1
XY is a straight beam, with B and C two points on it. Two equal rafters AB and AC meet at the ridge A. Angle ABX is 155°. Find the angle at the ridge, angle BAC.
XY is a straight beam, with B and C two points on it. Two equal rafters AB and AC meet at the ridge A. Angle ABX is 150°. Find the angle at the ridge, angle BAC.
XY is a straight beam, with B and C two points on it. Two equal rafters AB and AC meet at the ridge A. Angle ABX is 130°. Find the angle at the ridge, angle BAC.
At the playground, XY is the straight ground line, with the swing frame's legs standing on it at B and C. The two sloping bars of the frame, AB and AC, are equal in length, meeting at the top bar at A. Angle ABX, between bar AB and the ground, is 135°. Find the angle at the top of the frame, angle BAC.
XY is the straight edge of the stage, with the music stand's feet resting on it at B and C. The two legs of the stand, AB and AC, are equal in length, meeting at the top at A. Angle ABX, between leg AB and the stage, is 150°. Find angle ACB.
At a stall in the market, XY is the straight ground line, with the clothes rack's legs standing on it at B and C. The two legs of the rack, AB and AC, are equal in length, meeting at the top at A. Angle ABX, between leg AB and the ground, is 155°. Find the angle at the top of the rack, angle BAC.
In the school library, XY is the straight floor line, with the step-ladder's feet resting on it at B and C. The two sides of the ladder, AB and AC, are equal in length, meeting at the top hinge at A. Angle ABX, between side AB and the floor, is 150°. Find the angle at the top of the ladder, angle BAC.
On the field, XY is a straight line marked on the grass, with the two lower struts of a kite frame touching it at B and C. The two struts, AB and AC, are equal in length, meeting at the top of the kite at A. Angle ABX, between strut AB and the line, is 115°. Find the angle at the top of the kite, angle BAC.
In the kitchen, XY is the straight floor line, with the ironing board's legs standing on it at B and C. The two legs of the board, AB and AC, are equal in length, meeting at the top at A. Angle ABX, between leg AB and the floor, is 115°. Find the angle at the top of the board, angle BAC.
XY is a straight groundsheet line at a campsite, with pegs B and C fixed along it. The tent poles AB and AC are equal in length, meeting at the top of the tent at A. Angle ABX, between pole AB and the ground, is 130°. Find angle ACB.
In art class, XY is the straight line on the floor where the easel's legs touch the ground, at points B and C. The two front legs of the easel, AB and AC, are equal in length, meeting at the top at A. Angle ABX, between leg AB and the floor, is 145°. Find angle ACB.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 155°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 155 = 25°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 25°
The three angles of a triangle add to 180°.∠BAC = 180 − 25 − 25 = 130°
That is the angle the question asked for.Angle BAC is 130°.
Angle BAC is 130°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you one base angle, the equal sides give you the other, and 180° gives you the apex.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 150°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 150 = 30°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 30°
The three angles of a triangle add to 180°.∠BAC = 180 − 30 − 30 = 120°
That is the angle the question asked for.Angle BAC is 120°.
Angle BAC is 120°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you one base angle, the equal sides give you the other, and 180° gives you the apex.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 140°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 140 = 40°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 40°
That is the angle the question asked for.Angle ACB is 40°.
Angle ACB is 40°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you angle ABC, and the equal sides hand it straight to angle ACB.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 130°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 130 = 50°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 50°
The three angles of a triangle add to 180°.∠BAC = 180 − 50 − 50 = 80°
That is the angle the question asked for.Angle BAC is 80°.
Angle BAC is 80°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you one base angle, the equal sides give you the other, and 180° gives you the apex.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 125°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 125 = 55°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 55°
That is the angle the question asked for.Angle ACB is 55°.
Angle ACB is 55°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you angle ABC, and the equal sides hand it straight to angle ACB.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 135°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 135 = 45°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 45°
The three angles of a triangle add to 180°.∠BAC = 180 − 45 − 45 = 90°
That is the angle the question asked for.Angle BAC is 90°.
Angle BAC is 90°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you one base angle, the equal sides give you the other, and 180° gives you the apex.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 150°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 150 = 30°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 30°
That is the angle the question asked for.Angle ACB is 30°.
Angle ACB is 30°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you angle ABC, and the equal sides hand it straight to angle ACB.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 155°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 155 = 25°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 25°
The three angles of a triangle add to 180°.∠BAC = 180 − 25 − 25 = 130°
That is the angle the question asked for.Angle BAC is 130°.
Angle BAC is 130°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you one base angle, the equal sides give you the other, and 180° gives you the apex.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 125°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 125 = 55°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 55°
The three angles of a triangle add to 180°.∠BAC = 180 − 55 − 55 = 70°
That is the angle the question asked for.Angle BAC is 70°.
Angle BAC is 70°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you one base angle, the equal sides give you the other, and 180° gives you the apex.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 150°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 150 = 30°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 30°
The three angles of a triangle add to 180°.∠BAC = 180 − 30 − 30 = 120°
That is the angle the question asked for.Angle BAC is 120°.
Angle BAC is 120°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you one base angle, the equal sides give you the other, and 180° gives you the apex.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 115°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 115 = 65°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 65°
The three angles of a triangle add to 180°.∠BAC = 180 − 65 − 65 = 50°
That is the angle the question asked for.Angle BAC is 50°.
Angle BAC is 50°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you one base angle, the equal sides give you the other, and 180° gives you the apex.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 115°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 115 = 65°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 65°
The three angles of a triangle add to 180°.∠BAC = 180 − 65 − 65 = 50°
That is the angle the question asked for.Angle BAC is 50°.
Angle BAC is 50°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you one base angle, the equal sides give you the other, and 180° gives you the apex.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 130°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 130 = 50°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 50°
That is the angle the question asked for.Angle ACB is 50°.
Angle ACB is 50°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you angle ABC, and the equal sides hand it straight to angle ACB.
The figure gives one angle, and every other angle has to be reached from it.∠ABX = 145°
X, B, C and Y are on one straight line, and angles on a straight line add to 180°.∠ABC = 180 − 145 = 35°
AB and AC are marked equal, so the triangle is isosceles and its two base angles are equal.∠ACB = ∠ABC = 35°
That is the angle the question asked for.Angle ACB is 35°.
Angle ACB is 35°.
The pattern. Each step is one rule applied to an angle you already know. The straight line gives you angle ABC, and the equal sides hand it straight to angle ACB.