The chords of the circle AC and BD intersect. Find the CAD angle if ABD = 30 degrees and ADC = 50 degrees.
| May 6, 2021 | education
Internal angle ABD is based on the chord AD, the degree of which is equal to two internal angles.
Arc AD = 2 * 30 = 60.
The internal angle ACD also rests on the arc AD, therefore, its size is equal to half the degree measure of the arc AD.
Angle АСD = АD / 2 = 60/2 = 30 cm.
Consider a triangle ACD, for which two interior angles are known, then:
Angle CAD = 180 – ADC – ACD = 180 – 50 – 30 = 100.
Answer: The value of the CAD angle is 100.
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