Question

find the measure of ∠chm.

Explanation:

Step1: Identify angle relationship

Angles \( \angle KHM = 3k + 60 \) and \( \angle CHM = 2k + 160 \) are supplementary (form a linear pair), so their sum is \( 180^\circ \).
\[ (3k + 60) + (2k + 160) = 180 \]

Step2: Solve for \( k \)

Combine like terms:
\[ 5k + 220 = 180 \]
Subtract 220 from both sides:
\[ 5k = 180 - 220 = -40 \]
Divide by 5:
\[ k = \frac{-40}{5} = -8 \]

Step3: Find \( \angle CHM \)

Substitute \( k = -8 \) into \( 2k + 160 \):
\[ 2(-8) + 160 = -16 + 160 = 144 \]

Answer:

\( 144^\circ \)