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

In $△ ORS$ , $∠ ROS = 18 0^{\circ} - 12 5^{\circ} = 5 5^{\circ}$ . So $∠ OSR = 18 0^{\circ} - 7 0^{\circ} - 5 5^{\circ} = 5 5^{\circ}$ . Since triangles are similar, $∠ OQP = ∠ ORS = 7 0^{\circ}$ .

Step-by-step working

1
$∠ ROS = 18 0^{\circ} - 12 5^{\circ} = 5 5^{\circ}$
0.5 marks
2
$∠ OSR = 18 0^{\circ} - 7 0^{\circ} - 5 5^{\circ} = 5 5^{\circ}$
0.5 marks
3
$∠ OQP = ∠ ORS = 7 0^{\circ}$
1 mark

Concepts used

similar trianglesanglestriangle properties

Approach

Step-by-step working

Concepts used

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