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Please help, how do I solve this question?

Please help, how do I solve this question?-example-1
User Anindis
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1 Answer

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21 votes

Answer:

m∠3 = 92°

m∠4 = 88°

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).

User Rodnaph
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