Question

In a cyclic quadrilateral ABCD, if angle A=3(angle C). Find angle A

Answer 1

A+C=180°
3C+C=180
4C=180
C=180/4
=45°
A=135°[sum of opposite angles of cyclic quadrilateral is180°]

Answer 2

Given:

In a cyclic quadrilateral ABCD, if angle A=3(angle C).

To Find:

Find angle A

Solution:

A quadrilateral is a 2-dimensional closed figure with 4 sides and a cyclic quadrilateral is a quadrilateral inscribed inside a circle with all 4 vertices touching the circle.

In a cyclic quadrilateral, the opposite angles are supplementary means that the sum of the opposite angle is equal to 180 degrees.

So angle A and angle C are opposite and is given that,

$\angle A=3\angle C$

And according to the property of cyclic quadrilateral we have,

[tex]\angle A+\angle C=180\\ 3\angle C+\angle C=180\\ \angle C=45[/tex]

Substituted the value of angle A, now as angle C is 45 finding the value of angle A that is,

[tex]\angle A=3*45\\ =135[/tex]

Hence, the value of angle A is 135 degrees.