Question

Two straight lines cross at a point.

b+c+d=280°
Work out the sizes of angles a, b, c and d.
a
b
d.
C
Not drawn accurately

Answer 1

• a = c = 80°
• b = d = 100°

Explanation:

You want the measures of the angles where lines cross if the sum of three of them is 280°.

Linear pair

Angle b and c form a linear pair, so ...

b + c = 180°

Substituting that into the given equation, we have ...

b + c + d = 280°

180° + d = 280°

d = 100°

Vertical angles

Angles in this figure that do not share a side are vertical angles, hence congruent.

b = d = 100°

c = 180° -b = 180° -100° = 80° . . . . using the linear pair relation

a = c = 80°