Question

in the adjoining fig. ABCD is a parallelogram and diagonals insect at o. find
1. angle CAD
2. angle ACD
3. angle ADC

Answer 1

As ABCD is a parallelogram

angle ADC = 30 + 46 = 76°

in traingle DOA

cad + 46 + 68 = 180

cad = 66°

angle doc = 180-68 (linear pair)

doc = 112°

in triangle doc

30+112+acd = 180

acd = 38°

angle adc = 30 + adb

adb = 46° (alternate interior angles AD || BC)

adc = 46+30

adc = 76

Hope it helps you