Question

Q5. In the given figure, O is the centre of the circle, and x = 20° and y = 30°. The value of angle t is:

• A. ${80}^0$
• B. ${90}^0$
• C. ${100}^0$
• D. ${120}^0$

Answer 1

The correct option is C

${100}^0$

By joining B and C as shown in the figure, we get ΔABC

$Now,\angle OBC=\angle OCB=({90}^0-\frac{t}{2})Also\angle BAC=\frac{1}{2}\angle BOC=\frac{t}{2}In△ABC,(90-\left(\frac{t}{2}\right)+{20}^{\circ })+(90-\left(\frac{t}{2}\right)+{30}^{\circ })+\left(\frac{t}{2}\right)={180}^{\circ }Or(90+20+90+30)=t/2={180}^{0}Or\frac{t}{2}={50}^{0}Ort-{100}^0$