Question

question 1 of 10
true or false? a circle could be circumscribed about the quadrilateral below.

Explanation:

Step1: Recall the condition for circum - scribing a circle

A necessary and sufficient condition for a convex quadrilateral \(ABCD\) to be cyclic (a circle can be circumscribed about it) is that the sum of opposite angles is \(180^{\circ}\).

Step2: Check the sum of opposite angles

For angles \(A\) and \(C\), \(\angle A=90^{\circ}\) and \(\angle C = 90^{\circ}\), so \(\angle A+\angle C=90^{\circ}+90^{\circ}=180^{\circ}\). For angles \(B\) and \(D\), \(\angle B = 120^{\circ}\) and \(\angle D=60^{\circ}\), so \(\angle B+\angle D=120^{\circ}+60^{\circ}=180^{\circ}\).

Answer:

A. True