Question

in the triangle below, ∠q is a right angle. suppose that m∠p=(5x - 3)° and m∠r=(4x - 15)°. (a) write an equation to find x. make sure you use an \=\ sign in your answer. equation: (b) find the degree measure of each angle. m∠p = ° m∠q = ° m∠r = °

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Since ∠Q = 90°, we have m∠P+m∠R + 90°=180°. Substituting m∠P=(5x - 3)° and m∠R=(4x - 15)° gives the equation (5x - 3)+(4x - 15)+90 = 180.
(5x−3)+(4x−15)+90 = 180

Step2: Simplify the left - hand side of the equation

Combine like terms: 5x+4x-3 - 15 + 90=180, which simplifies to 9x+72 = 180.
9x+72 = 180

Step3: Solve for x

Subtract 72 from both sides: 9x=180 - 72, so 9x = 108. Then divide both sides by 9: x = 12.
9x=108, x = 12

Step4: Find the measure of ∠P

Substitute x = 12 into the expression for m∠P: m∠P=(5x - 3)°=(5×12 - 3)°=(60 - 3)° = 57°.
m∠P=(5×12 - 3)=57°

Step5: Recall the measure of ∠Q

m∠Q = 90° (given as a right - angle)
m∠Q = 90°

Step6: Find the measure of ∠R

Substitute x = 12 into the expression for m∠R: m∠R=(4x - 15)°=(4×12 - 15)°=(48 - 15)° = 33°.
m∠R=(4×12 - 15)=33°

Answer:

(a) Equation: (5x - 3)+(4x - 15)+90 = 180
(b)
m∠P = 57°
m∠Q = 90°
m∠R = 33°