Question

True or False? A circle could be circumscribed about the quadrilateral below.

Answer 1

Answer:

The answer is False.    

Step-by-step explanation:

Given a quadrilateral ABCD with angles ∠A=90°, ∠B=90°, ∠C=115° and ∠D=65°

We have to tell about the statement true or false

'A circle could be circumscribed about the quadrilateral'

As, we say a circle can be circumscribed about the quadrilateral  if and only if the quadrilateral is cyclic and also if the opposite angles of a quadrilateral are supplementary, then only the quadrilateral is cyclic.

Hence, we have to check for the opposite angles of quadrilateral if they are supplementary then we say the above statement is true i.e A circle could be circumscribed about the quadrilateral.

∠A+∠C=90+115=205° ≠ 180°

⇒ opposite angles are not supplementary.

∴ A circle could not be circumscribed about the quadrilateral.

The above statement is false.

Answer 2

Answer: false

Step-by-step explanation: the answer is false because suplimentary angled dont add up to 180