Question

Find the size of the angle marked a and b on the diagram

Answer 1

a = 52°

b = 38°

Explanation:

We know:

Angles in a triangle sum to 180°.

Therefore:

52° + 90° + b = 180°

142° + b = 180° |-142°

b = 38°

(look at the picture)

a + b = 90° ⇒ a + 38° = 90° |-38°

a = 52°

or

Angles 52° and a, are alternate interior angles. Therefore they are congruent.

a = 52°

Answer 2

Explanation:

we know that the total angles around the big triangle are 180° so, we know the right angle is 90° and we are told that one of the angles is 52° so just find the last angle by

180 = 90 + 52 + X

180 - 90 - 52 = X

38 = X

b = 38°

a = 52°