2. ∠2, ∠3, and ∠4 are interior angles of a triangle. M∠2 = 38°, M∠3 = 60°. What is the measure of ∠4?

To find the measure of angle ∠4 in a triangle when the measures of angles ∠2 and ∠3 are given, you can use the fact that the sum of the interior angles of a triangle is always 180°.
Here are the steps to solve this problem:

Understand the property of a triangle:

The sum of the interior angles in any triangle is 180°.


Write the equation based on the triangle angle sum property:

If M∠2 = 38° and M∠3 = 60°, then: M ∠2 + M ∠3 + M ∠4 = 180° Substitute the known values in the equation: 38° + 60° + M ∠4 = 180°


Calculate the measure of ∠4:

Combine the known angle measures: 98° + M ∠4 = 180°
Subtract 98° from both sides to find M∠4: M ∠4 = 180° − 98° M ∠4 = 82°



So, the measure of angle ∠4 is 82°.

Answered by LucasMatthewHarris | 2025-07-20