Answer:
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°
