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In triangle ABC, if AC is congruent to CB, angle A = 3x + 18, angle B = 7x - 58, & angle C = 2x - 8, find x & the measure of each angle.

Respuesta :

Blacklash

Answer:

        Angle A = 75°

        Angle B = 75°

        Angle C = 30°

Explanation:

  If AC is congruent to CB, from figure given we have angle A = angle B.

  Angle A = 3x + 18

  Angle B = 7x - 58

  Angle C = 2x - 8

We have,

        3x + 18 = 7x - 58

         4x = 76

          x = 19

So,

        Angle A = 3*19 + 18 = 75°

        Angle B = 7*19 - 58 = 75°

        Angle C = 2*19 - 8 = 30°

Ver imagen Blacklash
MrRoyal

Triangle ABC is an isosceles triangle.

  • The value of x is 19
  • The measure of each angle is 75, 75 and 30 degrees

The given parameters are:

[tex]\mathbf{AC = CB}[/tex]

[tex]\mathbf{\angle A =3x + 18}[/tex]

[tex]\mathbf{\angle B =7x - 58}[/tex]

[tex]\mathbf{\angle C =2x - 8}[/tex]

Because [tex]\mathbf{AC = CB}[/tex], then:

[tex]\mathbf{\angle A = \angle B}[/tex]

So, we have:

[tex]\mathbf{3x + 18 = 7x - 58}[/tex]

Collect like terms

[tex]\mathbf{7x - 3x = 18 + 58}[/tex]

[tex]\mathbf{4x = 76}[/tex]

Divide through by 4

[tex]\mathbf{x = 19}[/tex]

Hence, the value of x is 19

Substitute 19 for x in [tex]\mathbf{\angle A =3x + 18}[/tex], [tex]\mathbf{\angle B =7x - 58}[/tex] and [tex]\mathbf{\angle C =2x - 8}[/tex]

So, we have:

[tex]\mathbf{\angle A= 3 \times 19 + 18 = 75}[/tex]

[tex]\mathbf{\angle B= 7 \times 19 - 78 = 75}[/tex]

[tex]\mathbf{\angle C= 2 \times 19 - 8 = 30}[/tex]

The measure of each angle is: 75, 75 and 30 degrees

Read more about angles in isosceles triangle at:

https://brainly.com/question/21736141

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