Find the measures of the geometric parts listed below

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

(w – 2.5)(w + 2.5)

(–4v – 9)(–4v + 9)

step-by-step explanation:

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.