Question

Two straight lines cross at a point.

b+c+d=290°
Work out the sizes of angles a, b, c and d.
a
b
d
C
Not drawn accurately

Answer 1

a = 70°

b = 110°

c = 70°

d = 110°

Explanation:

The lines are straight, that makes two consecutive angles supplementary, which means their sum is 180°.

If b + c = 180, we can rewrite the expression b + c + d = 290°:

180° + d = 290°

• Subtract 180° from both sides to isolate d.

m∠d = 110°

angles a and d are also supplementary, so to find the measure of m∠a we can write the following equation:

a + 110° = 180°

• Subtract 110° from both sides to isolate a.

m∠a = 70°

Angles ∠b and angle ∠d are congruent angles so both angles are 110°.

Also, angle ∠c and angle ∠a are congruent angles so both angles 70°.