Answer:
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
- 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.
[tex] \large{ \tt{❈ \: SOLUTION}} : [/tex]
- Re-read the second point which I have mentioned above. Now , Set up an equation and solve for ∠ BGC .
[tex] \large{ \tt{{ ♡ \: \angle \: AGB + \angle \: BGC \: + \angle \: DGC = 180 \degree}}}[/tex] [ Sum of angle in a straight line ]
[tex] \large{ \tt{⟶ \: 30 \degree + m \angle \:BGC \: + \: 50 \degree = 180 \degree}}[/tex]
[tex] \large{ \tt{⟶ \: m \angle \: BGC + 80 \degree = 180 \degree}}[/tex]
[tex] \large{ \tt{⟶ \: m \angle \:BGC= 180 \degree - 80 \degree}}[/tex]
[tex] \large {\tt{⟶ \: m \angle \: BGC = 100 \degree}}[/tex]
- Hence , m ∠ BGC = 100°. Now , Re-read the third point which I have mentioned above and set up an equation and solve for x.
[tex] \large{ \tt{❊ \: 2x = 100 \degree}}[/tex] [ being vertically opposite angles ]
[tex] \large{ \tt{⇢\frac{2x}{2} = \frac{100 \degree}{2} }}[/tex]
[tex] \large{ \tt{⇢ \: x = 50 \degree}}[/tex]
- The value of x is 50°. Now :
[tex] \large{ \tt{❁ \: REPLACING \: VALUE : }}[/tex]
[tex] \large{ \tt{ ➝ \: \angle \: EGF = 2x \degree = 2 \times 50 = \boxed{ \tt{100 \degree}}}}[/tex]
[tex] \boxed{ \boxed{ \large{ \tt{☄ \: OUR \: FINAL \: ANSWER : \boxed{ \underline{100 \degree}}}}}}[/tex]
- Hence , Our final answer is 100° . And we're done!
[tex] \large{ \mathfrak{\# \: StayInAndExplore !\:☂ }}[/tex]
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