In the figure, lines m and n are parallel to each other. lines p and q are also parallel to each other. what is the value of x?

The value of x is 100°.

Step-by-step explanation:

It is given that lines m and n are parallel to each other. Lines p and q are also parallel to each other.

It a transversal line intersect two parallel line, then the corresponding angles are same. The angle with measure 100° and angle 2 are corresponding angles.

               (Corresponding angles)

It a transversal line intersect two parallel line, then the opposite exterior angles are same. The angle 3 and angle 2 are opposite exterior angles.

             (Opposite exterior angles)

Therefore the value of x is 100°.

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°