Question

for each part, just put the number. dont put x = # or a degree symbol or the word degree or the words, \i got...\ what is the value of p? what is the measure of the angle with the red arrow pointing at it? what is the measure of the angle with the blue arrow pointing at it?

Explanation:

Step1: Identify angle - relationship

The blue - arrowed angle is a right - angle, so the red - arrowed angle and the blue - arrowed angle are complementary (sum to 90 degrees).

Step2: Set up equation

Since the red - arrowed angle is $(3p - 6)^{\circ}$ and the blue - arrowed angle is 90 degrees, and they are complementary, we have the equation $3p-6 + 90=180$ (a straight - line is 180 degrees, and the sum of the two adjacent angles is 180). But since they are complementary, we can also set up $3p - 6=90$.

Step3: Solve for p

Add 6 to both sides of the equation $3p-6 = 90$:
$3p=90 + 6$
$3p=96$
Divide both sides by 3:
$p=\frac{96}{3}=32$

Step4: Find the measure of the red - arrowed angle

Substitute $p = 32$ into the expression for the red - arrowed angle $(3p - 6)^{\circ}$.
$3\times32-6=96 - 6=90$

Step5: Measure of the blue - arrowed angle

The blue - arrowed angle is a right - angle, so its measure is 90.

Answer:

1. 32
2. 90
3. 90