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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