Solve for value of y.

y = 6

General Formulas and Concepts:

A box at an angle signifies a 90° angle.

Step-by-step explanation:

Step 1: Set up equation

The 2 angles are Complementary Angles. They must add up to 90°.

(6y + 5) + (8y + 1) = 90

Step 2: Solve for y

y = 6

Step-by-step explanation:

So, the two angles sum up to 90 degrees.

Based on that, form an equation;

6y + 5 + 8y + 1 = 90

simplify,

6y + 5 + 8y + 1 = 90

14y + 6 = 90

inverse operations,

14y + 6 = 90

      -6     -6

14y = 84

/14     /14

y = 6

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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step-by-step explanation: