The value of m ∠ RPS is 64. 7°
<h3>What are collinear angles?</h3>
Collinear angles are angles formed when three or more points lie on the same straight line.
Note that angles on a straight line sum up to 180 degrees.
From the diagram given, we can see that the angles are collinear angles and thus sum up to 180 degrees;
- m ∠QPS = 88°
- m ∠ RPS = 5x + 34°
- m ∠ QPR = 8x + 15°
m ∠QPS + m ∠ RPS + m ∠ QPR = 180°
88° + 5x + 34° + 8x + 15° = 180
collect like terms
5x + 8x = 180 - 137
Add like terms
13x = 43
Make 'x' the subject of formula
x = 43/ 7
x = 6. 14
m ∠ RPS = 5x + 34 = 5 ( 6. 14) + 34 = 30. 7 + 34 = 64. 7°
Thus, the value of m ∠ RPS is 64. 7°
Learn more about collinear points here:
brainly.com/question/3307641
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The expression of the equation 4(x - 8) + y = 9(x - 2) in slope intercept form is; y = 5x + 14
<h3>How to write an equation in Slope Intercept form?</h3>
We want to express 4(x - 8) + y = 9(x - 2) in slope intercept form of y = mx + b.
Let us expand the equation to get;
4x - 32 + y = 9x - 18
Isolate y to get;
y = 9x - 4x - 18 + 32
y = 5x + 14
Thus;
Slope = 5
y - intercept = 14
x - intercept = -2.8
Read more about Slope Intercept Form at; brainly.com/question/1884491
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I have attached an image of the process I used