Unit Test nit Test Active 1 Angle PSR measures 99°. What is the measu 9° 24° 45° 54° P (3x + 18)° (9x – 27)° R S Mark this and return
The Correct Answer and Explanation is:
To find the measure of the angle at PPP given that the angle at PSRPSRPSR measures 99°, we can use the angle relationships and algebraic expressions provided.
We have the following angles:
- ∠PSR=99∘\angle PSR = 99^\circ∠PSR=99∘
- ∠P=(3x+18)∘\angle P = (3x + 18)^\circ∠P=(3x+18)∘
- ∠R=(9x−27)∘\angle R = (9x – 27)^\circ∠R=(9x−27)∘
Since angles PPP, SSS, and RRR form a linear pair (they lie on a straight line), the sum of the angles PPP, SSS, and RRR should equal 180°. So, the equation we can use is: ∠P+∠PSR+∠R=180∘\angle P + \angle PSR + \angle R = 180^\circ∠P+∠PSR+∠R=180∘
Substituting the known values into the equation: (3x+18)+99+(9x−27)=180(3x + 18) + 99 + (9x – 27) = 180(3x+18)+99+(9x−27)=180
Now, simplify the equation step by step: 3x+18+99+9x−27=1803x + 18 + 99 + 9x – 27 = 1803x+18+99+9x−27=180 (3x+9x)+(18+99−27)=180(3x + 9x) + (18 + 99 – 27) = 180(3x+9x)+(18+99−27)=180 12x+90=18012x + 90 = 18012x+90=180
Now, solve for xxx: 12x=180−9012x = 180 – 9012x=180−90 12x=9012x = 9012x=90 x=9012=7.5x = \frac{90}{12} = 7.5x=1290=7.5
Now that we know x=7.5x = 7.5x=7.5, we can substitute this value back into the expressions for ∠P\angle P∠P and ∠R\angle R∠R: ∠P=3(7.5)+18=22.5+18=40.5∘\angle P = 3(7.5) + 18 = 22.5 + 18 = 40.5^\circ∠P=3(7.5)+18=22.5+18=40.5∘ ∠R=9(7.5)−27=67.5−27=40.5∘\angle R = 9(7.5) – 27 = 67.5 – 27 = 40.5^\circ∠R=9(7.5)−27=67.5−27=40.5∘
Thus, the measure of ∠P\angle P∠P is 40.5° and the measure of ∠R\angle R∠R is 40.5°. Both of these angle measures check out with the sum of 180°, as: 40.5+99+40.5=180∘40.5 + 99 + 40.5 = 180^\circ40.5+99+40.5=180∘
The correct answer is ∠P=40.5∘\angle P = 40.5^\circ∠P=40.5∘.
