Question

In ΔPQR, \overline{PR} PR is extended through point R to point S, \text{m}\angle QRS = (10x-1)^{\circ}m∠QRS=(10x−1) ∘ , \text{m}\angle RPQ = (3x+17)^{\circ}m∠RPQ=(3x+17) ∘ , and \text{m}\angle PQR = (2x+12)^{\circ}m∠PQR=(2x+12) ∘ . Find \text{m}\angle QRS.M∠QRS.

Answer 1

<QRS = 55 degrees

Explanation:

Given the following

m∠QRS=(10x−1) ∘

∠RPQ=(3x+17) ∘

m∠PQR=(2x+12)

External angle m<QRS = 10x-1

Interior angles are m∠RPQ=(3x+17) ∘ and m∠PQR=(2x+12)

Using the law that the sum of interior angle is equal to exterior

10x + 1 = 3x+17 + 2x + 12

10x+1 = 5x+29

10x-5x = 29-1

5x = 28

x = 28/5

x = 5.6

Get m<QRS

Recall that <QRS = 10x - 1

<QRS = 10(5.6) - 1

<QRS = 56-1

<QRS = 55 degrees