Answer:
Part a) The measure of angle BDC is
Part b) The measure of angle CPD is
Part c) The measure of arc AD is
Part d) The measure of arc AB is
Part e) The measure of arc CAD is
Part f) The measure of angle ABD is
Step-by-step explanation:
Part a) Find the measure of angle BDC
we know that
The inscribed angle is half that of the arc it comprises.
substitute the value
Part b) Find the measure of angle CPD
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees.
so In the triangle CPD
substitute the values
Part c) Find the measure of arc AD
we know that
The inscribed angle is half that of the arc it comprises.
substitute the values
Part d) Find the measure of arc AB
Remember that BD is a diameter
so
----> the diameter divide the circle into two equal parts
Part e) Find the measure of arc CAD
we know that
substitute the values
Part f) Find the measure of angle ABD
we know that
The inscribed angle is half that of the arc it comprises.
substitute the values