Answer:
m ∠Q = 90°
m ∠ R = 37°
m ∠ S = 53°
Step-by-step explanation:
Given the right ΔRQS, where:
m ∠ Q = 90°
m ∠ R = (5x - 13)°
m ∠ S = (3x + 23)°
Since the sum of all the angles of a triangle add up to 180°, we can set up the following equation to find the value of x and the measures of each angle:
m ∠ Q + m ∠ R + m ∠ S = 180°
90° + (5x - 13)° + (3x + 23)° = 180°
90° + 5x° - 13° + 3x° + 23° = 180°
Combine like terms:
100° + 8x = 180°
Subtract 100° from both sides:
100° - 100° + 8x = 180° - 100°
8x° = 80°
Divide both sides by 8:
[tex]\frac{8x}{8} = \frac{80}{8}[/tex]
x = 10°
Substitute the value of x to find the measure of each angle:
m ∠ Q = 90°
m ∠ R = (5x - 13)° = 5(10) - 13 = 37°
m ∠ S = (3x + 23)° = 3(10) + 23 = 53°
