Question

true or false? a circle could be circumscribed about the quadrilateral below.
a. true
b. false

Explanation:

Step1: Recall cyclic quadrilateral rule

A quadrilateral is cyclic (can have a circumscribed circle) if and only if the sum of each pair of opposite angles is $180^\circ$.

Step2: Calculate sum of $\angle A$ and $\angle C$

$\angle A + \angle C = 90^\circ + 90^\circ = 180^\circ$

Step3: Calculate sum of $\angle B$ and $\angle D$

$\angle B + \angle D = 68^\circ + 112^\circ = 180^\circ$

Step4: Verify cyclic condition

Both pairs of opposite angles sum to $180^\circ$, so the quadrilateral is cyclic.

Answer:

A. True