The angle measure of the base angles of an isosceles triangle are represented by x and the vertex angle is 3x + 10. Find the measure of a ba

Question

The angle measure of the base angles of an isosceles triangle are represented by x and the vertex angle is 3x + 10. Find the measure of a base angle. a. 112° b. 42.5 c. 340 d. 16°​

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Đan Thu 5 years 2021-07-31T22:43:45+00:00 1 Answers 504 views 1

Answers ( )

  1. Nick
    1
    2021-07-31T22:45:23+00:00
    Reply

    Note: In option c, it must be 34°​ instead of 340.

    Given:

    Base angles of an isosceles triangle are represented by x.

    The vertex angle is 3x + 10.

    To find:

    The measure of a base angle.

    Solution:

    We know that, base angles of an isosceles triangle are equal. So, base angles are x and x.

    According to the angle sum property of triangles, the sum of all interior angles of a triangle is 180 degrees.

    Using angle sum property of triangles, we get

    x+x+(3x+10)=180

    5x=180-10

    5x=170

    Divide both sides by 5.

    x=\dfrac{170}{5}

    x=34

    The measure of base angle is 34 degrees. Therefore the correct option is c.

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