Answer:
Therefore, m∠6 is 115 degrees and m∠2 is 50 degrees.
Explanation:
To find m∠6, we need to use the fact that the sum of the measures of the angles in a triangle is 180 degrees.
From the given information, we know that m∠1 is 115 degrees. We also know that ∠1 and ∠6 are vertical angles, which means they are congruent. Therefore, m∠6 is also 115 degrees.
Now, we can use the fact that angles ∠1, ∠2, and ∠6 form a triangle to find the measure of ∠2.
The sum of the measures of the angles in a triangle is 180 degrees, so:
m∠1 + m∠2 + m∠6 = 180
Substituting the known values, we get:
115 + m∠2 + 115 = 180
Simplifying, we get:
m∠2 = 180 - 115 - 115
m∠2 = 50
Therefore, m∠6 is 115 degrees and m∠2 is 50 degrees.