Question

If m BEF = 100 and m CBE = 75, what is m DAG?

Answer 1

`\(m \, \text{DAG} = 25\)`This method follows the principles of geometry where angles within a straight line sum up to 180 degrees, and supplementary angles total 180 degrees when combined.

Explanation:

The angle measurement of ∠BEF is 100 degrees, and ∠CBE is 75 degrees. As angles on a straight line add up to 180 degrees, the total of angles ∠BEF and ∠CBE is 175 degrees (100 + 75 = 175). Therefore, to find the measure of ∠DAG, subtract the sum of angles ∠BEF and ∠CBE from 180 degrees (180 - 175 = 5 degrees). Since ∠DAG is supplementary to ∠CBE, subtracting 5 degrees from 180 degrees gives us an angle measurement of 25 degrees for ∠DAG.

Understanding angle relationships within a triangle is crucial here. As ∠BEF and ∠CBE are given, their sum is calculated to determine the remaining space within the straight line. The supplementary relationship between ∠DAG and ∠CBE aids in finding the measure of ∠DAG by subtracting the known angle (∠CBE) from 180 degrees.

This method follows the principles of geometry where angles within a straight line sum up to 180 degrees, and supplementary angles total 180 degrees when combined. Therefore, the measure of ∠DAG is 25 degrees based on the given information.