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

u what ?

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: