Finding Angle Measurement in Shifted Triangle
In the given figure, there is a triangle APB with a 45° angle at A. It's stated that point A is shifted to point B along the ray PX such that PB = 2PA. We're asked to find the measure of ∠BPY.
When point A is moved to point B, since PB is twice PA, triangle PBY will be an isosceles triangle where PB = PY. Therefore, the angles opposite the equal sides (PB and PY) will also be equal. Let's denote the measure of these angles as ∠PBY and ∠BPY, respectively.
Because the sum of angles in a triangle is always equal to 180°, we can use this rule to find the measure of ∠BPY.
For triangle PBY:
∠PBY + ∠BPY + ∠B = 180°
Since ∠PBY and ∠BPY are equal (isosceles triangle), we can say:
2∠BPY + 45° = 180°
Now, we solve for ∠BPY:
2∠BPY = 180° - 45°
2∠BPY = 135°
Dividing both sides by 2 gives us:
∠BPY = 135° / 2
∠BPY = 67.5°
So, the measure of ∠BPY is 67.5°, which is greater than 45°.
The correct answer is:
a) Greater than 45°
