Question

9. ABCD is a cyclic quadrilateral.
m(arc ABC) = 220° then
find angleABC, CDA and CBE.​

Answer 1

Answer:

firstly use inscribed angle theorem and get angle ADC

then get angle CBE by exterior angle of cyclic quadrilateral

get angle D +angle B =180.....by cyclic quadrilateral theorem

and substitute the value of angle D .....which we got frm inscribed angle..........hence proved

mark it as a brinliest answer

Answer 2

The values of the angles are $\angle CDA=110^{\circ}$ , $\angle ABC= 70^{\circ$ and $\angle CBE= 110^{\circ}$

Explanation:

Given that ABCD is a cyclic quadrilateral.

It is also given that $m({arc} \ A B C)=220^{\circ}$

We need to find the angles CDA, ABC and CBE

To find $\angle C D A$:

By inscribed angled theorem, we have,

$\angle A D C=\frac{1}{2} \ m({arc\ ABC})$

$\angle A D C=\frac{1}{2}\left(220^{\circ}\right)$

$\angle A D C=110^{\circ}$

Thus, the value of $\angle C D A$ is 110°

To find $\angle A B C$:

Since, we know that the opposite angles of a cyclic quadrilateral are supplementary, we have,

$\angle A B C+\angle A D C=180^{\circ}$

   $\angle A B C+110^{\circ}=180^{\circ}$

               $\angle A B C=70^{\circ}$

Thus, the value of $\angle A B C$ is 70°

To find $\angle C B E$:

The angles $\angle A B C$ and $\angle C B E$ are linear pairs.

Thus, we have,

$\angle A B C+\angle C B E=180^{\circ}$

     $70^{\circ}+\angle C B E=180^{\circ}$

               $\angle C B E=110^{\circ}$

Thus, the value of $\angle C B E$ is 110°

Learn more:

(1) In a cyclic quadrilateral ABCD, twice the measure of angle A is thrice the measure of angle C, find measure of angle C

brainly.in/question/5409195

(2) In give figure (15.90),PQRS is a cyclic quadrilateral .Find the measure of each of its angles.

brainly.in/question/7105950