2026 · Basic · Set 1 · Part 2·Q25·2 marks

Triangles

Question

In the given figure, $△ OSR \sim △ OQP$ , $∠ ROQ = 12 5^{\circ}$ and $∠ ORS = 7 0^{\circ}$ . Find the measures of $∠ OSR$ and $∠ OQP$ .

Approach

Using angle sum property and properties of similar triangles with corresponding angles being equal, find the required angles.

Step-by-step working

1
$∠ SOR = 18 0^{\circ} - 12 5^{\circ} = 5 5^{\circ}$ (linear pair)
0.5 marks
2
In $△ OSR$ : $∠ OSR = 18 0^{\circ} - 7 0^{\circ} - 5 5^{\circ} = 5 5^{\circ}$
0.5 marks
3
Since triangles are similar: $∠ OQP = ∠ ORS = 7 0^{\circ}$
1 mark

Concepts used

similar trianglesangle propertiescorresponding angles

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