ABCD is a cyclic quadrilateral, AB is the diameter of the circle and AB is parallel to DC. If angle ABC = 55°, then angle CAD equals
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ABCD is a cyclic quadrilateral, AB is the diameter of the circle and AB is parallel to DC. If angle ABC = 55°,
Answer:
Step-by-step explanation:
In a cyclic quadrilateral, opposite angles are supplementary, which means that the sum of the measures of opposite angles equals 180 degrees.
Given that angle ABC is 55 degrees, you can find angle ADC as follows:
Angle ADC = 180 degrees - Angle ABC
Angle ADC = 180 degrees - 55 degrees
Angle ADC = 125 degrees
So, angle CAD is also equal to 125 degrees because angle ADC and angle CAD are opposite angles in the cyclic quadrilateral.
Answer:
Step-by-step explanation:
In a cyclic quadrilateral, the opposite angles are supplementary. This means that if angle ABC is 55 degrees, then angle CAD, which is opposite to angle ABC, must be supplementary to it. Supplementary angles add up to 180 degrees.
So, to find angle CAD, you can subtract 55 degrees from 180 degrees:
CAD = 180° - ABC = 180° - 55° = 125°
Therefore, angle CAD is 125 degrees.