Question

use the image below to find the requested values. find the measure of ∠cmh.

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, meaning they add up to 180°. ∠TMC and ∠CMH are a linear - pair.

Step2: Set up the equation

Since ∠TMC = 116° and ∠TMC+∠CMH = 180°, we have 116°+(k + 50)°=180°.

Step3: Solve for k

First, simplify the left - hand side of the equation: 116 + k+50=180, which becomes k + 166 = 180. Then subtract 166 from both sides: k=180 - 166=14.

Step4: Find the measure of ∠CMH

Substitute k = 14 into the expression for ∠CMH. ∠CMH=(k + 50)°. So ∠CMH=(14 + 50)°=64°.

Answer:

64°