Quadrilateral ABCD is inscribed in the circle. Which sentence is true?
A) A and B are supplementary
B) A and C are supplementary
C) m∠A = m∠B
D) m∠C = m∠D

A) A and B are supplementary

Step-by-step explanation:

we know that

For any inscribed  quadrilateral in the circle , opposite angles will be supplementary

so

In this problem

Angle A and Angle B are supplementary angles

Angle B and Angle D are supplementary angles

therefore

The sentences that are true

A) A and B are supplementary

stop using this to cheat on home work

step-by-step explanation:

dfbvfvdf

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°