Question

Given square ABCD. Two isosceles triangles ABP and BCQ are constructed with bases

AB
and
BC
. Each of these triangles has vertex angle of 80°. Point P lies in the interior of the square, while point Q lies outside of the square. Find the angle measure between
PQ
and
BC

Answer 1

42 DEGREES

Explanation:

Answer 2

The angle measure between PQ and BC is 80°.

Let's denote the angle between PQ and BC as θ.

Since triangles ABP and BCQ are isosceles triangles with vertex angles of 80°, the base angles of these triangles are (180° - 80°) / 2 = 50° each.

Now, angle APQ is equal to the sum of angles APB and BPQ. Similarly, angle BCQ is equal to the sum of angles BQC and BCQ.

Since angles APB and BQC are both 50°, angle APQ + angle BCQ = 50° + 50° = 100°.

Therefore, the angle between PQ and BC, which is θ, is given by:

θ = 180° - (angle APQ + angle BCQ)

= 180° - 100°

= 80°.

So, the angle measure between PQ and BC is 80°.