Question

in figure angle A is equal to 60 degree and angle abc is equals to 80 find angle DPC and Angle BQC

Answer 1

Answer:

Step-by-step explanation:

Angle A+ Angle DCB =180° (opposite side of a cyclic quadrilateral is supplementary)

Therefore angle DCB=120°

Similarly angle ADC = 100°

AP is a straight line angle ADC + PDC=180°(linear pair)

Therefore angle CDA = 80°

Similarly angle PCD=60°

Angle CDA+PCD+DPC=180°(angle sum property of a triangle

Therefore angle DPC=40°

Angle DCB = 120° previously found

Angle ABC =80° given

As DQ is a straight line DCB+BCQ=180°(linear pair)

Therefore angle BCQ=60°

Similarly angle CBQ =100°

In triangle CBQ

angle BCQ+CBQ+BQC=180°(angle sum property)

Therefore angle angle BCQ=20°