Question

If ZKLM and ZPQR are complementary, and m∠KZM = 4x - 3 and m∠PQR = x + 13, which is m∠KZM?

Answer 1

The measure of angle KZM is 61 degrees. This is found by setting up the equation 4x - 3 + x + 13 = 90, as the angles are complementary, simplifying and solving for x, then substituting back into the expression for m∠KZM.

Step-by-step explanation:

When two angles ZKLM and ZPQR are complementary, the sum of their measures is 90 degrees. We have been given m∠KZM = 4x - 3 and m∠PQR = x + 13. To find the measure of angle KZM, we use the property of complementary angles which gives us the equation 4x - 3 + x + 13 = 90. Solving this:

1. Add coefficients of x: 4x + x = 5x.
2. Combine constants: -3 + 13 = 10.
3. Insert these into the equation: 5x + 10 = 90.
4. Subtract 10 from both sides: 5x = 80.
5. Divide both sides by 5: x = 16.
6. Now, substitute x back into the expression for m∠KZM: m∠KZM = 4(16) - 3 = 64 - 3 = 61 degrees.

Therefore, the measure of angle KZM is 61 degrees.