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Home > CCG > Chapter 5 > Lesson 5.2.1 > Problem 5-53

5-53.

Use the relationships found in each of the diagrams below to solve for and . Assume the diagrams are not drawn to scale. State which geometric relationships you used.

  1. Two triangles connected at a single vertex by extending two sides of the first and enclosing the second by a line segment. The triangle at the left has angles 70 degrees and 41 degrees. The triangle at the right has 58 degrees and x degrees. The third angle for each triangle is opposite angles that are in common between them. Angle, y, is supplement of the unknown angle for either triangle.

    Solve for the missing angle in the triangle with and . Use the Triangle Angle Sum Theorem to solve for the missing angle.

    and the angle are supplementary angles, because they form a linear pair.

    The angle and the angle across from it are vertical angles and vertical angles are congruent.

    Using the Triangle Angle Sum Theorem and the triangle on the right, so

  1. Two parallel lines are cut by a line segment (transversal) forming a, z, shape.  Another shorter segment from the bottom right side of the parallel line coming upward at an angle to the transversal encloses a triangle. The base angles of the triangle are 47 degrees at the left and 32 degrees at the right. Angle, y, is the supplement of the third interior angle. Angle, x, is the alternate interior angle of 47 degrees.

    ,

  1. 2 transversal lines, 1 at the top & 1 at the bottom, crosses 2 downward slanting parallel lines. The intersection of these lines in degrees: the top transversal & the far left parallel line: the exterior top angle is 83. The top transversal & the far right parallel line: the exterior bottom angle is y. The bottom transversal & the far left parallel line: the exterior top angle is x. The bottom transversal & the far right parallel line: the exterior top angle is 127.

    Find the measures of any angles that may relate to the unknown angles by using the angles given.

  1. A triangle with side lengths of 3 on left side, x on right side and y on bottom side. 45 degrees angle is in between the left side and right side. Another 45 degrees angle between the bottom side and right side.

    This is a special right triangle. Try drawing it to scale and then solve for and .