Question

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Answer 1

Answer:

Q5

As the opposite angles of a cyclic quadrilateral, A is supplementary with C and B is supplementary with D.

In the trapezoid,  angle A is supplementary with D and angle B is  supplementary with C.

It means ∠A ≅ ∠B and ∠D ≅ ∠C

Now, ∠ABD ≅ ∠ACD as both angles intercept same arc AD.

So we have:

• m∠B = m∠ABD + m∠DBC = 35° + 72° = 107°
• and
• m∠C = 180° - m∠B = 180° - 107° = 73°

So angles B and A are 107° and angles D and C are 73°

Q6

PXR is exterior angle of triangle XSR.

Angles Q and S are supplementary as opposite angles of a cyclic quadrilateral QPSR.

• m∠PXR = m∠XRS + m∠XSR = 20° + (180° - 80°) = 120°