What is the value of x?

x = 30 degrees

Step-by-step explanation:

Okay so we start by noticing that the two pointed out vertices = 180 degrees. So we have the following equation.

(x + 12) + (3x + 48) = 180

If you combine them you get:

4x + 60 = 180

Subtract 60 from both sides..

4x = 120

Divide both sides by 4..

x = 30

And there's your answer!

for b its (t) and c its (d)

step-by-step explanation:

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°