Solve for the value of Z

z = 13°

Step-by-step explanation:

Given the complementary angles, < (5z - 6)° and (2z + 5)°, whose measures add up to 90°:

We can solve for the value of z by establishing the following equation:

< (5z - 6)° + < (2z + 5)° = 90°

5z - 6 + 2z + 5 = 90°

Add like terms:

7z - 1 = 90°

Add 1 to both sides of the equation:

7z - 1 + 1 = 90° + 1

7z = 91°

Divide both sides by 7 to solve for z:

7z/7 = 91°/7

z = 13°

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54

step-by-step explanation:

6x9

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°