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°