Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

In circle A below, chord BC and diameter DAE intersect at F. If arc CD = 46° and arc BE = 78°, what is m_BFE? D B А​

Sagot :

Given:

Consider the below figure attached with this question.

In circle A below, chord BC and diameter DAE intersect at F.

The arc CD = 46° and arc BE = 78°.

To find:

The measure of angle BFE.

Solution:

According to intersecting chords theorem, if two chords intersect inside the circle then the angle on the intersection is the average of intercepted arcs.

Using intersecting chords theorem, we get

[tex]m\angle BFE=\dfrac{1}{2}(m(arcCD)+m(arcBE))[/tex]

[tex]m\angle BFE=\dfrac{1}{2}(46^\circ+78^\circ)[/tex]

[tex]m\angle BFE=\dfrac{1}{2}(124^\circ)[/tex]

[tex]m\angle BFE=62^\circ[/tex]

Therefore, the measure of angle BFE is 62°.

View image erinna
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.