MCQ
In the given figure, $ABCD$ and $ABEF$ are two cyclic quadrilaterals. If $\angle\text{BCD}=110^\circ$ then $\angle\text{BEF}=?$
- A$55^\circ$
- B$70^\circ$
- C$90^\circ$
- ✓$110^\circ $
✓
Answer
Correct option: D.
$110^\circ $
Since $ABCD$ is a cyclic qyadrilateral, we have:
$\angle\text{BAD}+\angle\text{BCD}=180^\circ$
$\Rightarrow\ \angle\text{BAD}+110^\circ=180^\circ$
$\Rightarrow\ \angle\text{BAD}=70^\circ$
Since $ABEF$ is a cyclic qyadrilateral, we have:
$\angle\text{BAD}+\angle\text{BEF}=180^\circ$
$\Rightarrow\ 70^\circ+\angle\text{BEF}=180^\circ$
$\Rightarrow\ \angle\text{BEF}=110^\circ$
$\angle\text{BAD}+\angle\text{BCD}=180^\circ$
$\Rightarrow\ \angle\text{BAD}+110^\circ=180^\circ$
$\Rightarrow\ \angle\text{BAD}=70^\circ$
Since $ABEF$ is a cyclic qyadrilateral, we have:
$\angle\text{BAD}+\angle\text{BEF}=180^\circ$
$\Rightarrow\ 70^\circ+\angle\text{BEF}=180^\circ$
$\Rightarrow\ \angle\text{BEF}=110^\circ$
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
Which one of the following statements is true?
In Fig. $\text{AB}\perp\text{BE}$ and $\text{FE}\perp\text{BE},$ If $\text{BC}=\text{DE}$ and $\text{AB}=\text{EF},$ then $\triangle\text{ABD}$ is congruent to:
→For the frequency distribution given below, the adjusted frequency for the class $25-45$ is:
→|
Class Interval
|
$5-10$
|
$10-15$
|
$15-25$
|
$25-45$
|
$45-75$
|
|
Frequency
|
$6$
|
$12$
|
$10$
|
$8$
|
$15$
|
A set of data consists of six numbers: $7, 8, 8, 9, 9,$ and $x.$ The difference between the modes when $x = 9$ and $x = 8$ is:
→Euclid stated that if equals are subtracted from equals, the remainders are equal in the form of:
The class mark of the class $100-120$ is:
→In the given figure, $O$ is the centre of the circle $ABE$ is a straight line. if $\angle\text{DBE}=95^\circ$ then $\angle\text{AOD}$ is equal to:
→A pyramid is a solid figure, whose base is:
$23 . \overline{43}$ when expressed in the form $\frac{p}{q}(p, q$ are integers $q \neq 0)$, is
→If $\sqrt{2^\text{n}}=1024,$ then $3^{2\Big(\frac{\text{n}}{4}-4\Big)}=$
→