MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sum of Pair of Opposite Angles in Quadrilateral

In the given ...

Question

In the given figure $□ M N O P$ is a cyclic quadrilateral. If $∠ P = 5 x + 12$ , and $∠ N = 3 x + 8$ then find the value of $x$ and also the measures of $∠ P$ and $∠ N$ .

Open in App

Solution

In a cyclic quadrilateral ,oppostie angles are supplimentary,
$∠ P + ∠ N = 180 5 x + 12 + 3 x + 8 = 180 8 x + 20 = 180 8 x = 160 x = 20 ∠ P = 5 (20) + 12 = 112 ∠ N = 3 (20) + 8 = 68$

Suggest Corrections

thumbs-up

0

Similar questions

Q. In the given figure,

M N O P

is a cyclic quadrilateral.
If

∠ P = 4 x + 12

∠ N = 3 x + 28

, then find the value of

x

and also the measures of

∠ P

∠ N

.

Q. Quadrilateral

M R P N

∠ R = {(5 x - 13)}^{o}, ∠ N = {(4 x + 4)}^{o}

, find measures of

∠ R

∠ N

Q. In the given figure, ABCD is a cyclic quadrilateral in which ∠BAD = 75°, ∠ABD = 58° and ∠ADC = 77°, AC and BD intersect at P. Then, find ∠DPC.

Q. Choose the correct answer from the alternatives given :
ABCD is a cyclic quadrilateral. Diagonals AC and BD meets at P. If

∠ A P B

110^{\circ}

∠ C B D

30^{\circ}

∠ A D B

P Q R S

is a cyclic quadrilateral. Find the measure of

∠ P

∠ Q

.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Circles and Quadrilaterals - Theorem 11

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Sum of Pair of Opposite Angles in Quadrilateral

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon