Question

Abcd is a cyclic trapezium with ab is parallel to cd and angle a is 105 degree then other angles are

Answer 1

ANGLE A = 105

ABIICD

ANGLE D = 180-105 ( co interior angle as ABIICD) = 75

ANGLE C = 180 - 105 ( OPPOSITE ANGLES OF CYCLIC QUADRILATERAL ARE SUPPLEMENTARY) = 75

ANGLE B = 180-75 ( co interior angle as ABIICD) = 105

Answer 2

Given:

AB is parallel to CD

Angle A=105°

To find:

All the other angles of the trapezium

Solution:

The measure of angle B= 105°, angle C=75°, and angle D=75°.

We can find the angles by following the given steps-

We know that ABCD is a cyclic trapezium.

So, the angles opposite to each other in this trapezium will be supplementary.

The sum of angle A and angle C=180° (1)

The sum of angle B and angle D=180° (2)

Now, we know that angle A=105°.

On putting the value of angle A in equation (1),

Angle A+Angle C=180°

105°+Angle C=180°

Angle C=180°-105°

Angle C=75°

Now, we know that the lines AB and CD are parallel.

So, the corresponding angles between parallel lines are also supplementary.

Angle A and Angle D are supplementary.

Angle A+ AngleD=180°

Putting the value of angle A,

105°+ Angle D=180°

Angle D=180°-105°

Angle D=75°

We will substitute the value of angle D in equation (2) to obtain the measure of angle B.

Angle B+ Angle D=180°

Angle B+75°=180°

Angle B=180°-75°

Angle B=105°

Therefore, the measure of angle B= 105°, angle C=75°, and angle D=75°.