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The vertex angle of an isosceles triangle is 42 more than 3 times the base angles. Find the vertex angle.

a The vertex angle is 124.8Β°.

b The vertex angle is 27.6Β°.

c The vertex angle is 40.8Β°.

d The vertex angle is 82.8Β°.​

Respuesta :

Answer: 124.8Β°

Step-by-step explanation:

1) Make an equation: [tex](3x+42)+x+x=180[/tex]

2) Expand and simplify the equation: [tex]5x+42=180[/tex]

3) Solve the equation:

Β  Β  Β a) [tex]5x= 138[/tex]

Β  Β  Β b) [tex]x= 27.6[/tex]

4) Substitute it into the original expression: 3x+42: [tex]3(27.6)+42= angle[/tex]

5) Solve the equation: [tex]angle= 124.8[/tex]

Answer:

a

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180Β°

let x be the base angles, then vertex angle is 3x + 42

Sum the 3 angles and equate to 180, that is

x + x + 3x + 42 = 180

5x + 42 = 180 ( subtract 42 from both sides )

5x = 138 ( divide both sides by 5 )

x = 27.6

Thus

vertex angle = 3x + 42 = 3(27.6) + 42 = 82.8 + 42 = 124.8Β° β†’ a

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