Question

In cyclic □ABCD, ∠B=75°, then find ∠D.​

Answer 1

Answer:

We know,

Opposite angles in a cyclic quadrilateral i.e. angle B+ angle D = 180 degrees

are supplementary.

Thus,

If angle B = 75 degrees

Then,

angle D = 180 - 75

angle D = 105 degrees

Answer 2

In cyclic □ABCD , ∠B = 75°, then ∠D = 105°

Given :

In cyclic □ABCD , ∠B = 75°

To find :

The measure of ∠D

Concept :

The sum of the opposite angles of a cyclic quadrilateral is 180°

Solution :

Step 1 of 2 :

Write down the measure of the given angle

Here it is given that in cyclic □ABCD , ∠B = 75°

Step 2 of 2 :

Find the measure of ∠D

It is given that ABCD is a cyclic quadrilateral

∴ The sum of a pair of two opposite angles will be 180°.

∠B + ∠ D = 180°

⇒ 75° + ∠D = 180°

⇒ ∠D = 180° – 75°

⇒ ∠D = 105°

Hence the measure of ∠D = 105°

Note : The figure is referred to the attachment

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