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3-34.

Examine the diagrams below. For each one, write and solve an equation to calculate the value of . Show all work.

  1. A triangle where all three sides have 1 tick mark. One angle interior angle is 4 x minus 12 degrees.

    Equilateral triangles have three congruent angles.

  1. A right triangle with a leg of 3.1, hypotenuse of 4.9, and second leg of x.

    This is a right triangle, so use the Pythagorean Theorem to solve for .

  1. A trapezoid with horizontal parallel bases. A diagonal from bottom left to top right creates 2 internal triangles. In degrees, top triangle has 51 and 103. The bottom triangle has 82 and x. The unknown angle in the top triangle is adjacent to 82 in the bottom triangle. The unknown angle in the bottom triangle is adjacent to 51 in the top triangle.


    Because and are alternate interior angles,
    they are congruent. Therefore, .

  1. A four sided figure where all four sides have 1 tick mark. Bottom side has a length of 2, x + 9 and right side has a length of 3, x minus 2.