Question

Given

m
∠
Q
P
S
=
8
8
∘
m∠QPS=88
∘
m, angle, Q, P, S, equals, 88, degrees
m
∠
R
P
S
=
5
x
+
3
4
∘
m∠RPS=5x+34
∘
m, angle, R, P, S, equals, 5, x, plus, 34, degrees
m
∠
Q
P
R
=
8
x
+
1
5
∘
m∠QPR=8x+15
∘
m, angle, Q, P, R, equals, 8, x, plus, 15, degrees
Find
m
∠
R
P
S
m∠RPSm, angle, R, P, S:

Answer 1

By applying the triangle sum theorem, which states that the sum of angles in a triangle is 180 degrees, the measure of angle RPS was found to be approximately 50.55 degrees after solving the system of equations for x.

Step-by-step explanation:

To find the measure of angle RPS, we need to consider that angles QPS, RPS, and QPR are parts of a triangle, and thus, by the triangle sum theorem, the sum of these angles should be 180 degrees.

Given:

• 
  
• m∠QPS = 88°

• m∠RPS = 5x + 34°

• m∠QPR = 8x + 15°
• 
  
• 
  

The triangle sum theorem states that the sum of the angles in a triangle is 180 degrees. Therefore:

m∠QPS + m∠RPS + m∠QPR = 180°

88° + (5x + 34°) + (8x + 15°) = 180°

Now we solve for x:

88 + 5x + 34 + 8x + 15 = 180

13x + 137 = 180

13x = 43

x = 43 / 13

x = 3.31

Now we plug x into the expression for m∠RPS:

m∠RPS = 5x + 34°

= 5(3.31) + 34°

= 16.55 + 34

= 50.55°

The measure of angle RPS is approximately 50.55 degrees.