If m∠PQR = 141 ° , find each measure.

m<PQS = 82°

m<RQS = 59°

Step-by-step explanation:

m<PQS = (13x + 4)°

m<RQS = (10x - 1)°

m<PQR = 141°

To find each angle measure, find the value of x.

First, get an equation that defines the relationship between the angle measures as follows:

m<PQS + m<RQS = m<PQR (angle addition postulate)

(13x + 4)° + (10x - 1)° = 141°

Use the equation to solve for x

13x + 4 + 10x - 1 = 141

Combine like terms

13x + 10x + 4 - 1 = 141

23x + 3 = 141

Subtract 3 from each side of the equation

23x + 3 - 3 = 141 - 3

23x = 138

Divide each side by 23

23x/23 = 138/23

x = 6

m<PQS = (13x + 4)°

Plug in the value of x

m<PQS = 13(6) + 4 = 78 + 4

m<PQS = 82°

m<RQS = (10x - 1)°

Plug in the value of x

m<RQS = 10(6) - 1 = 60 - 1

m<RQS = 59°