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Given triangle DEF where ∠D = (7b +1)∘, ∠E = (2b + 1)∘, and ∠F = ( b + 8)∘. What is the measure of ∠E?

Given triangle DEF where D 7b 1 E 2b 1 and F b 8 What is the measure of E class=

Respuesta :

Answer:  35 (choice C)

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Explanation:

For any triangle, the three interior angles always add to 180.

D+E+F = 180

(7b+1) + (2b+1) + (b+8) = 180

(7b+2b+b) + (1+1+8) = 180

10b+10 = 180

10b = 180-10

10b = 170

b = 170/10

b = 17

Use this value of b to find the three angle measures

  • D = 7b+1 = 7*17+1 = 119+1 = 120
  • E = 2b+1 = 2*17+1 = 34+1 = 35 degrees
  • F = b+8 = 17+8 = 25

As a check,

D+E+F = 120+35+25 = 120+60 = 180

which helps confirm the correct answers.

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