Here's how to find the values of angles x, y, and m: a) To find angle x: Angle x is ∠ POQ. Step 1: Identify the type of triangle OPQ. Since O is the center of the circle, OP and OQ are both radii. Therefore, OPQ is an isosceles triangle with OP = OQ. Step 2: Determine the base angles of OPQ. In an isosceles triangle, the angles opposite the equal sides are equal. So, ∠ OQP = ∠ OPQ. Given ∠ OPQ = 24°, thus $∠ OQP = 24

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A) To find angle x:

April 29, 2026Mathematics

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Here's how to find the values of angles $x$ , $y$ , and $m$ :

a) To find angle $x$ :
Angle $x$ is $\angle POQ$ .

Identify the type of triangle $\triangle OPQ$ .
Since $O$ is the center of the circle, $OP$ and $OQ$ are both radii. Therefore, $\triangle OPQ$ is an isosceles triangle with $OP = OQ$ .
Determine the base angles of $\triangle OPQ$ .
In an isosceles triangle, the angles opposite the equal sides are equal. So, $\angle OQP = \angle OPQ$ .
Given $\angle OPQ = 24^\circ$ , thus $\angle OQP = 24