Prove that the angle pqr is a right angle
Pls show full working out ty

A missing bit of information is that ABCD must be a rectangle.

First, let's gather some facts:

(1) Angles in a triangle add up to 180.

(2) RQC and PBQ are the same triangles since it is given that their sides are equal.

(3) Also ∠PBQ = ∠QCR are 90° since they are in fact the corners of the rectangle.

(4) ∠PQB, ∠PQR and∠RQC are on the same line, so their sum must be 180°

Putting it all together, we can say for both triangles using (1):

∠RQC + ∠QRC + ∠QCR = 180 and ∠QCR=90 => ∠RQC = 90-∠QRC

∠PBQ + ∠BQP + ∠PQB = 180

Furthermore, since both triangles are equal (2):

∠QRC = ∠PQB

So, ∠RQC = 90 - ∠PQB

Finally, using (4) we can say:

∠PQB + ∠PQR +  90 - ∠PQB = 180.

Simplify that and you get:

∠PQR +  90 = 180

∠PQR =  90

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

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