AB is the diameter of a circle with Centre O and CD parallel to AB. If angle DAB= 25°, then find the measure of the angle CAD
Answers
Answer:
40
Step-by-step explanation:
Given AB is the diameter of a circle with Centre O and CD parallel to AB. If angle DAB= 25°, then to find the measure of the angle CAD
AB is the diameter of the circle. We can take angle ADB = 90 degree since it is a semi circle.
It is given angle DAB = 25 = angle CDA (because alternate angles)
We get ABCD as a cyclic quadrilateral if all lines are drawn.
Now angle CDB = angle CDA + angle ADB = 25 + 90 = 115 degree
angle CAB + angle CDB = 180 (cyclic quadrilateral)
angle CAB + 115 = 180
CAB = 180 - 115 = 65 degree
DAB + CAD = CAB
25 + CAD = 65
CAD = 65 - 25
CAD = 40 degree.
The measure of the angle CAD is 40 degree.
Answer:
40
Step-by-step explanation:
Given AB is the diameter of a circle with Centre O and CD parallel to AB. If angle DAB= 25°, then to find the measure of the angle CAD
AB is the diameter of the circle. We can take angle ADB = 90 degree since it is a semi circle.
It is given angle DAB = 25 = angle CDA (because alternate angles)
We get ABCD as a cyclic quadrilateral if all lines are drawn.
Now angle CDB = angle CDA + angle ADB = 25 + 90 = 115 degree
angle CAB + angle CDB = 180 (cyclic quadrilateral)
angle CAB + 115 = 180
CAB = 180 - 115 = 65 degree
DAB + CAD = CAB
25 + CAD = 65
CAD = 65 - 25
CAD = 40 degree.
The measure of the angle CAD is 40 degree.
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