Question

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Lines AB and CD A Type the answers into the boxes below. The measure of angle FBA is The measure of angle BAF is are parallel. Find the measures of the three angles in triangle ABF E The measure of angle AFB is с 42° F B 157° D​

Answer 1

The measure of angle FBA is 42°

The measure of angle BAF is 23°

The measure of angle AFB is 115°

Explanation:

Alternate angles are two angles that are formed on opposite sides of a transversal line that intersects two parallel lines. Alternate interior angles are the angles that are inside the two parallel lines, and alternate exterior angles are the angles that are outside the two parallel lines. and they are congruent to each other.

A linear pair is a pair of adjacent angles that add up to 180 degrees.

The sum of interior angles of a triangle is 180 degrees

In this case:

m ∠FBA is alternate angle of m ∠BCD.

Therefore, m ∠FBA = 42°

Again,

m∠CDE and m ∠CDF are linear pair,

So,

m∠CDE + m ∠CDF = 180°

Substituting value:

157° + m ∠CDF = 180°

m ∠CDF = 180° - 157°

m ∠CDF = 23°

Since

m ∠CDF is alternate angle of m ∠BAF.

Therefore, m ∠BAF = 23°

And

In ∆ ABF

m∠BAF + m ∠FBA + m ∠AFB = 180°

Substituting value:

23° + 42° + m ∠AFB = 180°

65° + m ∠AFB = 180°

m ∠AFB = 180° - 65°

m ∠AFB = 115°

Therefore,

The measure of angle FBA = 42°

The measure of angle BAF = 23°

The measure of angle AFB = 115°