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PQRS is a rhombus in which ∠SPQ = 64°. Equilateral triangles PXQ and QYR are drawn outside the rhombus on sides PQ and QR. Calculate the magnitude of the angle ∠QXY.
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- 26°
- 28°
- 30°
- 45°
- 26°
Correct Option: B
As per the given in question , we draw a figure of a rhombus PQRS and Equilateral triangles PXQ and QYR are drawn outside the rhombus on sides PQ and QR
∠SPQ = 64°
∴ ∠PQR + ∠SPQ = 180°
∠PQR = 180° – 64° = 116°
As we know that each angle of equilateral triangle is 60°.
∴ ∠XQY = 360° – 116° – 60° – 60° = 124°
| ∴ ∠QXY = | = | = 28° | ||
| 2 | 2 |
