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Find the measure of the exterior angle. *

Find The Measure Of The Exterior Angle class=

Sagot :

TheAnimeGirl

Step-by-step explanation:

✧ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \: O \: N}}} }: [/tex]

  • Set up an equation and solve for x :

⋆ [tex] \large{ \bf{(4x + 9) \degree = 2x \degree + (3x - 12) \degree}} [/tex] [ Exterior angle is always equal to the sum of two non - adjacent interior angles ]

~Remove the unnecessary brackets

⟶ [tex] \large{ \bf{4x \degree + 9 \degree = 2x \degree + 3x \degree - 12 \degree}}[/tex]

~Add the like terms : 2x ° & 3x°

⟶ [tex] \large{ \bf{4x \degree + 9 \degree = 5x \degree - 12 \degree}}[/tex]

~Move 4x to right hand side and change it's sign

~Similarly move 12 to left hand side and change it's sign

⟶ [tex] \large{ \bf{9 \degree + 12 \degree = 5x \degree - 4x \degree}}[/tex]

⟶ [tex] \large{ \bf{21 \degree = x \degree}}[/tex]

⟶ [tex]{ \large{ \bf{x = 21 \degree}}}[/tex]

  • Now , Substituting the value of x in (4x+9)° [ Exterior angle ]

⤿ [tex] \large{ \bf{4 \times 21 \degree + 9 \degree}} = \boxed{93 \degree}[/tex]

☥ [tex] \boxed{ \boxed{ \large{ \tt{Our \: Final \: Answer : \boxed{ \underline { \tt{93\degree}}}}}}}[/tex]

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Answer:

exterior angle=4x+9=4×21+9=93

Step-by-step explanation:

2x+3x-12=4x+9 exterior angle is equal to the sum of two opposite interior angle of the triangle

5x-4x=12+9

x=21

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