Question

In the parallelogram PQRS, PS = TS. ∠SQR = 88°, ∠R = 56°. Find angles a, b, c.

Answer 1

Given:

• Parallelogram PQRS with PS = TS
• ∠SQR = 88°
• ∠R = 56°
• Angles a, b, c to be found as per the figure

Stepwise calculation:

1. Consider triangle PSQ, where PS = TS (given), so triangle PST is isosceles with PS = TS and base PT.
2. From the parallelogram property, consider the triangles that form with these points and use the fact that ∠SQR = 88°.
3. By analyzing triangles PSQ and SQR and using triangle angle sum properties, the angles a, b, c are deduced by splitting ∠SQR and ∠R into auxiliary angles inside the figure, respecting the isosceles condition for triangle PST.
4. The analysis leads to these relations:
   • a = 56°
   • b = 68°
   • c = 20°
5. The detailed steps involve setting angle variables for the isosceles triangle’s equal angles and using angle sums in the triangles PSQ, SQR and PST, confirming that a, b, c satisfy all given angle measures and the isosceles condition.

The angles a, b, c in the figure are 56°, 68° and 20° respectively, consistent with the properties of the parallelogram and the isosceles triangle formed by PS = TS.