Question

In the given figure, $△ O D C \sim △ OB A$ . If $∠ BOC = 110º$ , $∠ O D C = 45º$ and $A B = 2 C D$ , then find (i) $m ∠ O A B$ (ii) $OB : O D$ .

Approach

Given $△ O D C \sim △ OB A$ with $∠ BOC = 110°$ , $∠ O D C = 45°$ , and $A B = 2 \cdot C D$ . (i) Using angle properties, $∠ O A B = 65°$ . (ii) From similarity ratio $\frac{O D}{OB} = \frac{D C}{B A} = \frac{1}{2}$ , so $OB : O D = 2 : 1$ .

Step-by-step working

1
(i) Since $△ O D C \sim △ OB A$ , $∠ O A B = 180° - 110° - 45° = 65°$
1 mark
2
(ii) $\frac{O D}{OB} = \frac{D C}{B A} = \frac{1}{2} \Rightarrow OB : O D = 2 : 1$
1 mark

Concepts used

similar trianglescorresponding anglesratio of sidesfind anglefind ratio

Approach

Step-by-step working

Concepts used

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