Question

Find the measure of the exterior angle. *

Answer 1

Explanation:

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`\underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \: O \: N}}} }:`

• Set up an equation and solve for x :

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

~Remove the unnecessary brackets

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`\large{ \bf{4x \degree + 9 \degree = 2x \degree + 3x \degree - 12 \degree}}`

~Add the like terms : 2x ° & 3x°

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`\large{ \bf{4x \degree + 9 \degree = 5x \degree - 12 \degree}}`

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

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

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`\large{ \bf{9 \degree + 12 \degree = 5x \degree - 4x \degree}}`

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`\large{ \bf{21 \degree = x \degree}}`

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`{ \large{ \bf{x = 21 \degree}}}`

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

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`\large{ \bf{4 * 21 \degree + 9 \degree}} = \boxed{93 \degree}`

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`\boxed{ \boxed{ \large{ \tt{Our \: Final \: Answer : \boxed{ \underline { \tt{93\degree}}}}}}}`

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Answer 2

exterior angle=4x+9=4×21+9=93

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