Mathematics

Question

In triangle ABC, the measure of angle B is 60 more than A. The measure of angle C is eight times the measure of A. If x represents the measure of angle A, set up and solve an equation to find the measure of angle A.

2 Answer

  • Answer: the measure of angle A is 12 degrees

    Step-by-step explanation:

    Let x represent the measure of angle A.

    Let y represent the measure of angle B.

    Let z represent the measure of angle C.

    In triangle ABC, the measure of angle B is 60 more than A. This means that

    y = x + 60

    The measure of angle C is eight times the measure of A. This means that

    z = 8x

    Also, the sum of the angles in a triangle is 180 degrees. Therefore

    x + y + z = 180 - - - - - - - - - 1

    Substituting y = x + 60 and z = 8x into equation 1, it becomes

    x + x + 60 + 8x = 180

    10x + 60 = 180

    10x = 180 - 60 = 120

    x = 120/10 = 12

  • Answer:

    Step-by-step explanation:

    measure of A=x

    ∠C=8x

    ∠B=x+60

    in a triangle sum of angles=180°

    x+8x+x+60=180

    10x=120

    x=12

    m∠A=12°

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