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Step-by-step explanation:

Given,

angle 1 = 52°

we know,

it is a complementry angle so,

angle 1 + angle 2 = 90°

as we know any angle which is exact 90° is known as complementary angle

so, after inserting the values we got,

→ 52° + angle 2 = 90°

→ angle 2 = 90° - 52°

→ angle 2 = 38°

therefore, value of Angle 2 is 38° .

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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°