Can someone help me with #24??

x = 10, y = 15

Step-by-step explanation:

(8x - 10) and 7x are alternate angles and congruent, thus

8x - 10 = 7x ( subtract 7x from both sides )

x - 10 = 0 ( add 10 to both sides )

x = 10

Then 7x = 7 × 10 = 70

(6y + 20) and 7x are adjacent angles and supplementary, thus

6y + 20 + 70 = 180 , that is

6y + 90 = 180 ( subtract 90 from both sides )

6y = 90 ( divide both sides by 6 )

y = 15

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°

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