Question

Given the following diagram, find the missing measure.

Given:



m P = m 2; m P =

30
45
60
90

Answer 1

Answer: b) 45

Explanation:

Answer 2

m∠P = 45°

Explanation:

If m∠P = m∠2 then it's an isosceles triangle.

m∠M = 90°, therefore it's an isosceles right triangle.

We know, the sum of measures of angles in a triangle is equal 180°.

Therefore we have the equation:

m∠P + m∠2 + m∠M = 180°

Substitute m∠M = 90° and m∠P = m∠2 = x:

x + x + 90° = 180° substract 90° from both sides

2x = 90° divide both sides by 2

x = 45° → m∠P = 45°