Question

In a cyclic quadrilateral pqrs if angle p - angle r =50, angle p and angle r

Answer 1

Answer:

Step-by-step explanation:

by given condition

p+r=180

p=180-r

second condition

p-r=50

put p =180-r in p-r=50

180-r-r=50

130=2r

r=65

p=180-r

p=180-65

p=115

Answer 2

Given:

Angle p-angle r=50°

To find:

The measure of angle p and r

Solution:

The measure of angle p is 115° and r is 65°.

We can find the measure by following the steps given below-

We know that pqrs is a cyclic quadrilateral.

The angles which are opposite to each other in a cyclic quadrilateral, their sum is 180°.

So, the sum of angle p and angle r is 180°.

angle p + angle r=180°

It is given to us that angle p - angle r=50°.

We will solve the set of equations by using the method of elimination.

The equations are as follows-

angle p + angle r=180°

angle p - angle r=50°

Adding both the equations, we get

2× angle p=230°

Angle p=230/2

Angle p=115°

Now, we will substitute the value of the angle p in any equation.

In the equation, angle p - angle r=50°, we put the value of angle p

115° - angle r=50°

115-50= Angle r

Angle r=65°

Therefore, the measure of angle p is 115° and r is 65°.