Question

In the given figure, $△ OSR \sim △ OQP$ , $∠ ROQ = 125°$ and $∠ ORS = 70°$ . Find the measures of $∠ OSR$ and $∠ OQP$ .

Approach

Using the exterior angle property, $∠ OSR = ∠ ROQ - ∠ ORS = 125° - 70° = 55°$ . Since the triangles are similar, corresponding angles are equal, so $∠ OQP = ∠ OSR = 55°$ .

Step-by-step working

1
$∠ OSR = 125° - 70° = 55°$ (by exterior angle property)
1 mark
2
As $△ OSR \sim △ OQP$ , $∠ OQP = ∠ OSR = 55°$ (corresponding angles)
0.5 marks
3
$∠ OQP = 55°$
0.5 marks

Concepts used

similarityanglesexterior angletriangles

Approach

Step-by-step working

Concepts used

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