ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°. Is the given statement true or false and justify your answer

Solution:

It is given that

ABCD is a cyclic quadrilateral

∠A = 90°

∠B = 70°

∠C = 95°

∠D = 105°

We know that

In a cyclic quadrilateral, the sum of opposite angles is 180°

It can be written as

∠A + ∠C = 90° + 95° = 185° ≠ 180°

∠B + ∠D = 70° + 105° = 175° ≠ 180°

Here the sum of opposite angles is not equal to 180°

So it is not a cyclic quadrilateral

Therefore, the statement is false.

✦ Try This: ABCD is a cyclic quadrilateral such that ∠A = 100°, ∠B = 80°, ∠C = 105° and ∠D = 75°.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10

NCERT Exemplar Class 9 Maths Exercise 10.2 Problem 7

ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°. Is the given statement true or false and justify your answer

Summary:

The statement “ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°” is false

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