Question

Consider the following diagram below.


Find the values of x and y.

Answer 1

The value of x is 17.

The value of y is 22.5.

Answer 2

x = 17, y = 22.5

Explanation:

In this question, we are asked to calculate the value of y and x.

Now, the circle theorem to use is that opposite angles of a cyclic quadrilateral are supplementary. This means that they add up to be 180 degrees.

Thus, mathematically;

(4x-3) + (6x+13) = 180

and also;

5y + 3y = 180

Thus, solving both equations one after the other, we can get the values of x and y.

Let’s start with the first;

4x -3 + 6x+13 = 180

10x + 10 = 180

10x = 180-10

10x = 170

x = 170/10

x = 17

For the second equation;

8y = 180

y = 180/8

y = 22.5