If p || q, solve for x.

The value of x is 8.

Solution:

Given line p is parallel to line q.

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

(11x - 5)° = (7x + 27)°

11x° - 5° = 7x°  + 27°

Add 5° on both sides.

11x° = 7x°  + 32°

Subtract 7x° from both sides.

4x° = 32°

Divide by 4 on both sides.

x° = 8°

x = 8

The value of x is 8.

y=1/4x-4

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°