Question

1. if m∠mkl = 83°, m∠jkl = 127°, and m∠jkm = (9x − 10)°, find the value of x.

Explanation:

Step1: Use angle addition postulate

We know that \( m\angle JKL = m\angle JKM + m\angle MKL \). Substituting the given values, we get \( 127 = (9x - 10) + 83 \).

Step2: Solve for x

First, simplify the right - hand side: \( (9x - 10)+83=9x + 73 \). So the equation becomes \( 127=9x + 73 \). Subtract 73 from both sides: \( 127 - 73=9x \), which is \( 54 = 9x \). Then divide both sides by 9: \( x=\frac{54}{9}=6 \).

Answer:

\( x = 6 \)