Question

Quadrilateral ABCD ​ is inscribed in this circle.

Answer 1

Rule: Opposite angles of inscribed quadrilaterals are supplementary.
In other words, the opposite angles of inscribed quadrilaterals add to 180 degrees.

A+C = 180
A+74 = 180 ................ plug in the given value for C
A+74-74 = 180-74 .... subtract 74 from both sides
A = 106

Angle A is 106 degrees

Answer 2

Answer:

Measure of ∠A is 106°

Step-by-step explanation:

We are given that, 'Quadrilateral ABCD is inscribed in the circle'.

So, we get that,

'ABCD is a cyclic quadrilateral' i.e. The sum of the opposite interior angles is 180°.

Thus, we have,

∠A +∠C = 180°

i.e. ∠A + 74° = 180°

i.e. ∠A = 180° - 74°

i.e. ∠A = 106°

Thus, the measure of ∠A is 106°.