Question 10b

WXYZ is a trapezium and PYR is an isosceles triangle where PY = YR. ∠WZY = 52°, ∠WQY = 74° and ∠QYR = 35°. Find ∠XYP. (2 marks)

$Question 10b diagram$

Answer: 61 °

Workings

Loading drawing…

∠ XYP is part of trapezium WXYZ

∠ XYP = ∠ XYZ (red) - ∠ PYQ (green)

∠ XYZ (red) = 180 - 52 = 128

∠ PYQ (green) is part isosceles triangle PYR

∠ PYQ (green) → ∠ PYR (orange) - 35

∠ PYR (orange) → 180 - ∠ YRP (red) x 2

∠ YRP is part of ▵ YQR

∠ YRP = 180 - 35 - ∠ YQR (blue)

∠ YQR (blue) → 180 - 74 = 106

∠ YRP = 180 - 35 - ∠ YQR (blue) = 180 - 35 - 106 = 39

∠ PYR (orange) → 180 - ∠ YRP (red) x 2 = 180 - 39 x 2 = 102

∠ PYQ (green) → ∠ PYR (orange) - 35 = 102 - 35 = 67

∠ XYP = ∠ XYZ (red) - ∠ PYQ (green) = 128 - 67 = 61°

1 video