Explanation:
To solve this problem, we need to use some basic trigonometry. We know that POQ is a straight line, which means that ∠QPS and ∠SPO must be equal. So, we have: 25° = ∠QPS = ∠SPO. Now, we can use the law of sines to find x and y. The law of sines states that the ratio of a side of a triangle to the sine of the angle opposite that side is the same for all sides. Therefore, we have: x/sin 25° = y/sin 25°. Solving for x
From the previous equation, we get: x = y × sin 25°. We also know that PQ = y + x, so: y + x = y × sin 25°. Subtracting y from both sides gives us: x = y × sin 25° - y. We can now plug in y to get: x = (20 - y) × sin 25°. And, solving for y, we get: y = 20 - (x × cos 25°). Finally, we have our two values: x = y × sin 25° - y and y = 20 - (x × cos 25
We can now find the values of x and y by plugging in the given values for the angles. For example, let's say that ∠QPS = 25° and ∠SPO = 55°. Then, we have: x = 55° × sin 25° - 55° = 11.94. And, y = 20 - 11.94 × cos 25° = 23.11. Therefore, x = 11.94 and y = 23.11. These values satisfy the condition that POQ is a straight line and SOP = 25°. Do you want to try another problem?