Answer:
m∠3 = 92°
m∠4 = 88°
Step-by-step explanation:
Note:
For this post, I will provide the solutions for finding the measures of ∠3 and ∠4.
Solution for m∠3
Given a triangle whose two nonadjacent interior angles have measures of m∠45° and m∠47°:
We can find the measures of ∠3 and ∠4 by applying the Exterior Angle Theorem which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of two nonadjacent interior angles.
In other words:
m∠3 = m∠45° + m∠47°
m∠3 = 92°
Therefore, the measure of m∠3 = 92°.
Solution for m∠4
In order to find the measure of ∠4, we could simply apply the Triangle Sum Theorem which states that the sum of all interior angles of a triangle is equal to 180°.
Since we have the measures of two nonadjacent interior angles, we can find the measure of ∠4 by performing the following steps:
m∠4 = 180° - (m∠45° + m∠47°)
m∠4 = 180° - 92°
m∠4 = 88°.
Therefore, m∠4 = 88°.
Double-check:
In order to verify whether we have the correct measures for ∠3 and ∠4, let us substitute all the given and derived values from the previous steps:
Apply the Triangle Sum Theorem:
m∠4° + m∠45° + m∠47° = 180°
88° + 45° + 47° = 180°
180° = 180° (True Statement).
