Question

Given trangle PAR, MZP = (6x + 4)", mZA = (2x - 15), and mZR = (42 - 1)'. Determine the measure of each

of the angles of the triangle and classify the triangle by side length and angle measure.

Answer 1

To determine the measure of each angle of the triangle PAR, set up an equation using the given angles and find the value of x. Then, substitute the value of x back into the angles to find their measures. Finally, classify the triangle based on its side lengths and angle measures.

Step-by-step explanation:

To determine the measure of each angle of the triangle PAR, we need to find the values of MZP, ZA, and ZR.

Given MZP = (6x + 4)°, ZA = (2x - 15)°, and ZR = (42 - 1)°.

To find x, we can set up an equation:
MZP + ZA + ZR = 180°
(6x + 4) + (2x - 15) + (42 - 1) = 180
8x + 30 + 41 = 180
8x + 71 = 180
8x = 180 - 71
8x = 109
x = 109/8

Substitute the value of x back into the given angles to find their measures:

MZP = (6 * 109/8 + 4)°
ZA = (2 * 109/8 - 15)°
ZR = (42 - 1)°

Now, calculate the values of MZP, ZA, and ZR. Once we have all the angle measures, we can classify the triangle by its side lengths and angle measures.