Find the value of X that will make L║M

x = 60

Step-by-step explanation:

Given: L ∥ M and the line going through them is transversal

The sum of the interior angles on the same side of a transversal is equal to 180 degrees; therefore, (2x + 5) degrees + (x - 5) degrees = 180 degrees.

2x + 5 + x - 5 = 180

2x + x + 5 - 5 = 180

3x + 0 = 180

3x = 180

x = 180/3

x = 60

Double Check:

2(60) + 5 + (60) - 5 = 180 degrees

120 + 5 + 55 =

125 + 55 =

180 degrees

180 degrees = 180 degrees

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°