Please answer this question now

m∠D = 94°

Step-by-step explanation:

Quadrilateral ABCD is also called a cyclic quadrilateral or a quadrilateral that is inscribed in a circle.

Opposite angles in a cyclic Quadrilateral are supplementary, i.e the sum of two opposite angles in a Quadrilateral = 180°

m∠A + m∠C = 180°

m∠A = 74°

74° + m∠C = 180°

m∠C = 180° - 74°

m∠C = 106°

In a cyclic quadrilateral, the total sum of the angles outside the circle = 360°

i.e =

m∠AB + m∠BC + mDC + mAD = 360°

m∠DAB= ( m∠C) × 2

= 106° × 2 = 212°

m∠DAB = m∠AD + m∠AB

m∠AD = 79°

212° = 79° + m∠AB

m∠AB = 212° - 79°

= 133°

m∠ABC = m∠AB + m∠BC

m∠AB = 133°

m∠BC= 55°

m∠ABC = 133° + 55°

= 188°

We are asked to find m∠D

m∠D = 1/2m∠ABC

m∠ABC = 188°

m∠D = 1/2 × 188°

m∠D = 94°

Therefore, m∠D = 94°