MCQ
Mark $(\checkmark)$ against the correct answer.In the given figure, $\text{AB}\parallel\text{CD,}\angle\text{OAB}=150^\circ$ and $\angle\text{OCD}=120^\circ.$ The $\angle\text{AOC}={}?$
- A$80^\circ$
- ✓$90^\circ$
- C$70^\circ$
- D$100^\circ$
✓
Answer
Correct option: B.
$90^\circ$
In the figure, $\text{AB}\parallel\text{CD}$
$\angle\text{OAB}=150^\circ,\angle\text{OCD}=120^\circ$
From $O$, draw $\text{OE}\parallel\text{AB}$ or $CD$
$\text{AB}\parallel\text{DE}$
$\angle\text{OAB}+\angle\text{AOE}=180^\circ$
$\Rightarrow150^\circ+\angle\text{AOE}=180^\circ$
$\Rightarrow\angle\text{AOE}=180^\circ-150^\circ=30^\circ$
Similarly $\text{DE}\parallel\text{CD}$
$\Rightarrow\angle\text{EOC}+\angle\text{OCD}=180^\circ$
$\Rightarrow\angle\text{EOC}+120^\circ=180^\circ$
$\Rightarrow\angle\text{EOC}=180^\circ-120^\circ=60^\circ$
Now $\angle\text{AOC}=\angle\text{AOE}+\angle\text{EOC}$
$=30^\circ+60^\circ=90^\circ$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
$(?) \div (-18) = -5$
→What is the additive identity element in the set of whole numbers?
Mark $(\checkmark)$ against the correct answer in the following:
Which of the following is a vulgar fraction?
→Which of the following is a vulgar fraction?
Mark against the correct answer in the following: If $\frac{\text{A}}{2}=\frac{\text{B}}{3}=\frac{\text{C}}{4}$ then $A : B : C = ?$
→Mark $(\checkmark)$ tick against the correct answer in the following:
$\bigg\{6^{-1}+\Big(\frac{3}{2}\Big)^{-1}\bigg\}=?$
→$\bigg\{6^{-1}+\Big(\frac{3}{2}\Big)^{-1}\bigg\}=?$
Mark against the correct answer in the following: If $7 : x :: 35 : 45$, then $x = ?$
→In Fig. $\text{AOB}$ is a straight line and the ray $\text{OC}$ stands on it. The value of $x$ is:
→The number $4,70,394$ is standard form is written as:
→Mark $(\checkmark)$ against the correct answer in the following: $0.5 \times 0.05 = ?$
→Mark $(\checkmark)$ tick against the correct answer in the following:
$\Big(\frac{2}{3}\Big)^{-5}=?$
→$\Big(\frac{2}{3}\Big)^{-5}=?$