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 $32^o$ , the measure of angle CFD is . ?

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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 $32^o$ , the measure of angle CFD is . ?

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Answer 1 · 2017-04-26T03:29:15

$angleCFD=119^@$

Explanation:

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

$angleBME=180-32-90=58^@$
$=> angleBMC=angleBME$
As $angleBMC$ is twice the $angleBDC$ ,
$=> angleBDC=58/2=29^@$

$=> angleCFD=180-angleACD-angleBDC$
$=180-32-29=119^@$

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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 $32^o$ , the measure of angle CFD is . ?

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Explanation:

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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^o32^o, the measure of angle CFD is . ?

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Explanation:

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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 $32^o$ , the measure of angle CFD is . ?