Question

In the figure below, ΔMNO≅ΔPQR.What is the measure of ∠P? Show your work and explain your reasoning.

Answer 1

`\huge\boxed{\sf P = 79.5\°}`

Step-by-step explanation:

Given that:

ΔMNO ≅ ΔPQR

That means

M ↔ P

N ↔ Q

O ↔ R

So,

∠P ≅ ∠M

Given that P = 3x + 20.4 and M = 5x - 19

3x + 20.4 = 5x - 19

Add 19 to both sides

3x + 20.4 + 19 = 5x

3x + 39.4 = 5x

Subtract 3x to both sides

39.4 = 5x - 3x

39.4 = 2x

2x = 39.4

Divide both sides by 2

x = 19.7

Given that:

P = 3x + 20.4

P = 3(19.7) + 20.4 (x = 19.7)

P = 59.1 + 20.4

P = 79.5°

`\rule[225]{225}{2}`

Hope this helped!

~AH1807