Question

In ΔPQR, \overline{PR} PR is extended through point R to point S, \text{m}\angle PQR = (2x+1)^{\circ}m∠PQR=(2x+1) ∘ , \text{m}\angle QRS = (10x-10)^{\circ}m∠QRS=(10x−10) ∘ , and \text{m}\angle RPQ = (3x+14)^{\circ}m∠RPQ=(3x+14) ∘ . What is the value of x?X?

Answer 1

Answer:

x = 5

Step-by-step explanation:

In ΔPQR, PR is extended through point R to point S.

m∠PQR=(2x+1) ∘

m∠QRS=(10x−10) ∘

m∠RPQ=(3x+14) ∘

Hence, we solve using Exterior angle Theorem.

This means that:

m∠QRS = m∠PQR + m∠RPQ

(10x - 10)° = (2x + 1)° + (3x + 14)°

10x - 10 = 2x + 1 + 3x + 14

Collect like terms

10x - 2x - 3x = 1 + 14 + 10

5x = 25

x = 25/5

x = 5