Question

IN APQR, if mZP is 14 less than five times x, mZQ is five less than x, and mZR is nine less

than twice x, find x and the measure of each angle.
mZP =
m2Q =
mZR ="

Answer 1

To find x and the measures of each angle in triangle APQR, we set up an equation based on the sum of interior angles of a triangle being 180 degrees. After solving for x, we determine that x = 26 and then calculate each angle measure accordingly: m∠P = 116°, m∠Q = 21°, and m∠R = 43°.

Step-by-step explanation:

In triangle APQR, we have the following relationships for the measures of the angles:

• m∠P = 5x - 14
• m∠Q = x - 5
• m∠R = 2x - 9

Since APQR is a triangle, we know that the sum of the interior angles should be 180 degrees. Therefore, we can create the following equation:

5x - 14 + x - 5 + 2x - 9 = 180

Combining like terms, we get:

8x - 28 = 180

Adding 28 to both sides gives us:

8x = 208

Dividing both sides by 8 to solve for x, we find:

x = 26

Using the value of x, we can now find the measures of each angle:

• m∠P = 5(26) - 14 = 130 - 14 = 116°
• m∠Q = 26 - 5 = 21°
• m∠R = 2(26) - 9 = 52 - 9 = 43°