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2 votes
Please ??????????????​

Please ??????????????​-example-1

2 Answers

6 votes
X=12
Angle A=35
And angle ABC=65
User Smdrager
by
6.5k points
5 votes

Answers:

  • x = 12
  • angle A = 35
  • angle ABC = 65

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Step-by-step explanation:

Let y be the measure of angle ABC.

We can see that y = 4x+17 because the two angles (y and 4x+17) are vertical angles. Vertical angles are always congruent.

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From here, focus entirely on the interior angles of triangle ABC.

Recall that for any triangle, the interior angles always add to 180

A+B+C = 180

(x+23)+(y)+(80) = 180 ..... plug in the given angle measures

(x+23)+(4x+17)+(80) = 180 .... replace y with 4x+17

5x+120 = 180 ..... combine like terms

5x = 180-120 ..... subtract 120 from both sides

5x = 60

x = 60/5 ..... divide both sides by 5

x = 12

Now use that x value to find the following:

  • angle A = x+23 = 12+23 = 35
  • angle ABC = y = 4x+17 = 4*12+17 = 48+17 = 65

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In short we have this summary of values we found:

  • x = 12
  • angle A = 35
  • angle ABC = 65
User David Pelaez
by
6.5k points
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