Question

Find m∠EGF. please help!

Answer 1

100°

Explanation:

Since ∠AD are 180°, and each side is the same,

180°-30°-50°=100°

Answer 2

`\large{ \tt{❃ \: EXPLANATION}} :`

• We're provided - ∠AGB = 30° , ∠ DGC = 50° and ∠ EGF = 2x. We're asked to find out m ∠ EGF.

• Note that ∠ AGB , ∠ BGC and ∠ DGC form a straight line which means that their sum is equal to 180°.

• When two lines intersect , the angles formed opposite to each other are called verticall opposite angles. Vertically opposite angle are always equal to each other.

`\large{ \tt{❈ \: SOLUTION}} :`

• Re-read the second point which I have mentioned above. Now , Set up an equation and solve for ∠ BGC .

`\large{ \tt{{ ♡ \: \angle \: AGB + \angle \: BGC \: + \angle \: DGC = 180 \degree}}}` [ Sum of angle in a straight line ]

`\large{ \tt{⟶ \: 30 \degree + m \angle \:BGC \: + \: 50 \degree = 180 \degree}}`

`\large{ \tt{⟶ \: m \angle \: BGC + 80 \degree = 180 \degree}}`

`\large{ \tt{⟶ \: m \angle \:BGC= 180 \degree - 80 \degree}}`

`\large {\tt{⟶ \: m \angle \: BGC = 100 \degree}}`

• Hence , m ∠ BGC = 100°. Now , Re-read the third point which I have mentioned above and set up an equation and solve for x.

`\large{ \tt{❊ \: 2x = 100 \degree}}` [ being vertically opposite angles ]

`\large{ \tt{⇢(2x)/(2) = (100 \degree)/(2) }}`

`\large{ \tt{⇢ \: x = 50 \degree}}`

• The value of x is 50°. Now :

`\large{ \tt{❁ \: REPLACING \: VALUE : }}`

`\large{ \tt{ ➝ \: \angle \: EGF = 2x \degree = 2 * 50 = \boxed{ \tt{100 \degree}}}}`

`\boxed{ \boxed{ \large{ \tt{☄ \: OUR \: FINAL \: ANSWER : \boxed{ \underline{100 \degree}}}}}}`

• Hence , Our final answer is 100° . And we're done!

`\large{ \mathfrak{\# \: StayInAndExplore !\:☂ }}`

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