Question

question
in the diagram below, find the value of x and y.
answer attempt 1 out of 2
x =
y =

Explanation:

Step1: Use the property of angles subtended by the same chord

The angle subtended by an arc at the center is twice the angle subtended at the circumference. Here, the angle at the center is \(34^{\circ}\), and the angle at the circumference \(x\) is related as \(x=\frac{34^{\circ}}{2}\).

$$x = 17^{\circ}$$

Step2: Use the property of angles in a triangle

In \(\triangle XYZ\), we know that the angle subtended by a diameter is a right - angle. So, \(3x + 2y=90^{\circ}\). Substitute \(x = 17^{\circ}\) into the equation:

$$3\times17+2y=90$$

$$51 + 2y=90$$

$$2y=90 - 51$$

$$2y=39$$

$$y = 19.5^{\circ}$$

Answer:

\(x = 17\), \(y=19.5\)