Answer :
(3x+5)+(x+3)=180
4x+8=180
4x=172
x=43
3(43)+5
<PQR=134
<SQR=46
Answer:
[tex]\boxed {\angle PQR = 134\textdegree}[/tex]
Step-by-step explanation:
Both angles are Supplementary (Two angles that add up to 180°). So, write an expression using the following measurements of both [tex]\angle PQR[/tex] and [tex]\angle RQS[/tex] and 180:
[tex]\angle PQR = 3x + 5[/tex]
[tex]\angle RQS = x + 3[/tex]
[tex]3x + 5 + x + 3 = 180[/tex]
Solve:
[tex]3x + 5 + x + 3 = 180[/tex]
[tex]4x + 5 + 3 = 180[/tex]
[tex]4x + 8 = 180[/tex]
[tex]4x + 8 - 8 = 180 - 8[/tex]
[tex]4x = 172[/tex]
[tex]\frac{4x}{4} = \frac{172}{4}[/tex]
[tex]x = 43[/tex]
-After you have the value of [tex]x[/tex], use it to the expression of [tex]\angle {PQR}[/tex] to get the actual answer of [tex]\angle PQR[/tex]:
-The value of [tex]x[/tex]:
[tex]x = 43[/tex]
-Solve for the measurement of [tex]\angle PQR[/tex]:
[tex]3x + 5[/tex]
[tex]3(43) + 5[/tex]
[tex]129 + 5[/tex]
[tex]134[/tex]
-The measurement of [tex]\angle PQR:[/tex]
[tex]\boxed {\angle PQR = 134\textdegree}[/tex]