Question

PLEASE HELP ASAP

Given: circle k(O), m FE =56°, FD=ED, m∠EFD=76°
Find: m∠EFO

Answer 1

Based on the inscribed isosceles triangle shown below, the measure of angle EFO is 62°.

In Euclidean Geometry, the measure of an intercepted arc is equal to the central angle of a circle. Based on the information provided above, the measure of arc FE is equal to 56°, so the measure of the central angle FOE must be equal to 56°.

By critically observing triangle FOE, we can logically deduce that it is an isosceles triangle with base FE because segments FO and EO represent the radii of circle O.

Since an isosceles triangle comprises two (2) side lengths that are equal and two (2) base interior angles that are congruent, we have:

FD = ED

m∠EFO ≅ m∠FEO

By applying triangle sum property to triangle FOE, we have;

m∠EFO + m∠FEO + mFE = 180°

2m∠EFO + m∠FE = 180°

2m∠EFO + 56° = 180°

m∠EFO = (180° - 56)/2

m∠EFO = 62°

Complete Question:

Given: circle k(O), m FE =56°, FD=ED, m∠EFD=76°

Find: m∠EFO

Answer 2

62°

Explanation:

If mEF=56°, then ∠EOF=56° as central angle subtended on the arc EF.

Consider isosceles triangle FOE (this triangle is isosceles, because OF=OE as radii of the circle k(O)). In this triangle, angles adjacent to the base EF are congruent. Since the sum of the measures of all interior angles in triangle is 180°, then

m∠EFO=m∠OEF=1/2(180°-56°)=62°.

Actually, point D is extra to solve this question.