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Option (3)

Step-by-step explanation:

            Statements                             Reasons

1). l ⊥ n                                        1). Given

2). ∠1 = 90°                                 2). Definition of perpendicular lines

3). m ⊥ n                                     3). Given

4). ∠2 = 90°                                4). Definition of perpendicular lines

5). ∠1 ≅ ∠2                                 5). Corresponding angles postulate

6). m∠2 = 90°                             6). Substitution property of equality

7). m ⊥ n                                     7). Definition of perpendicular lines

Hence, Option (3) will be the correct option.

correct

step-by-step explanation:

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°