Question

Find the value of the largest angle in △OCB if ∠OCB and ∠OBC are in the ratio 2:3.

• A. 48°
• B. 36°
• C. 90°
• D. 72°

Answer 1

The correct option is D 72°


$\angle COB=\angle DOA={60}^{\circ }$ (vertically opposite angles)
$\angle OCB:\angle OBC=2:3$ (given)
$\therefore \text{Let}\angle OCB=2x\angle OBC=3x$

$\text{In}△OCB2x+3x+{60}^{\circ }={180}^{\circ }\Rightarrow 5x={180}^{\circ }-{60}^{\circ }\Rightarrow x=\frac{{120}^{\circ }}{5}={24}^{\circ }$
$\therefore$ The largest angle $=\angle OBC={72}^{\circ }$