Question

HELP ASAPPPP. Thanks!!!

Answer 1

The correct option is (d) that is

`\bf \implies{m \angle{EHF} = 31 \degree}`

Explanation:

Given:

`\bigg( \bf \angle{DHE} \: and \: \angle{EHF} \: are \: \\ \bf{complementary \: angles} \bigg)`

To Find:

`{ \bf \longrightarrow{m \angle{EHF} = \: ? }}`

Solution:

We know that,

• Two angles are said to be complementary, if the sum of their measures is 90°.
• Two complementary angles are called the complement of each other.
• For example :- Angles measuring 55° and 35° are complementary angles because measure of their sum is 90°

According to the question,

`\bf \longrightarrow{6x - 1+ 3x + 1 = 90 \degree}`

`\bf \longrightarrow{6x \cancel{- 1} + 3x \cancel{+ 1 }= 90 \degree}`

`\bf \longrightarrow{6x + 3x = 90 \degree}`

`\bf \longrightarrow{9x = 90 \degree}`

`\bf \longrightarrow{x = \frac{ \cancel{90} \degree}{ \cancel{9}} }10 \degree`

`\bf \longrightarrow{x = 10 \degree}`

`{ \bf \longrightarrow{m \angle{EHF} = \: 3 * 10 \degree + 1 \mapsto31 \degree }}`

So, the correct option is (d)

`\bf \longrightarrow{m \angle{EHF} = 31 \degree}`