Answer:
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°
