In the figure, M is a center of the circle, F is the intersection of the lines AC and BD, and E is the intersection of the lines CM and BD. The line CM is perpendicular to the line BD. If the measure of angle MBE is $32^{o}$ $32^o$ , the measure of angle CFD is . ?

Question

In the figure, M is a center of the circle, F is the intersection of the lines AC and BD, and E is the intersection of the lines CM and BD. The line CM is perpendicular to the line BD. If the measure of angle MBE is $32^{o}$ $32^o$ , the measure of angle CFD is . ?

1 Answer

Impact of this question

1729 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-26T03:29:15

$∠ C F D = 119^{\circ}$ $angleCFD=119^@$

Explanation:

enter image source here

As $A, B, C, and D$ $A, B, C, and D$ lie on the circle, they are cyclic quadrilateral.
$\Rightarrow ∠ A B D = ∠ A C D$ $=> angleABD=angleACD$ as they subtends the same arc.
Given $∠ M B E = 32^{\circ},$ $angle MBE=32^@,$
$\Rightarrow ∠ A B D = ∠ A C D = ∠ M B E = 32^{\circ}$ $=> angle ABD=angleACD=angleMBE=32^@$

$∠ B M E = 180 - 32 - 90 = 58^{\circ}$ $angleBME=180-32-90=58^@$
$\Rightarrow ∠ B M C = ∠ B M E$ $=> angleBMC=angleBME$
As $∠ B M C$ $angleBMC$ is twice the $∠ B D C$ $angleBDC$ ,
$\Rightarrow ∠ B D C = \frac{58}{2} = 29^{\circ}$ $=> angleBDC=58/2=29^@$

$\Rightarrow ∠ C F D = 180 - ∠ A C D - ∠ B D C$ $=> angleCFD=180-angleACD-angleBDC$
$= 180 - 32 - 29 = 119^{\circ}$ $=180-32-29=119^@$

Science

Math

Humanities

... and beyond

In the figure, M is a center of the circle, F is the intersection of the lines AC and BD, and E is the intersection of the lines CM and BD. The line CM is perpendicular to the line BD. If the measure of angle MBE is $32^{o}$ $32^o$ , the measure of angle CFD is . ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

In the figure, M is a center of the circle, F is the intersection of the lines AC and BD, and E is the intersection of the lines CM and BD. The line CM is perpendicular to the line BD. If the measure of angle MBE is 32o32^o, the measure of angle CFD is . ?

1 Answer

Explanation:

Related questions

Impact of this question

In the figure, M is a center of the circle, F is the intersection of the lines AC and BD, and E is the intersection of the lines CM and BD. The line CM is perpendicular to the line BD. If the measure of angle MBE is $32^{o}$ $32^o$ , the measure of angle CFD is . ?