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Home > GC > Chapter 7 > Lesson 7.1.1 > Problem 7-7

7-7.

A triangle has angles in degrees, B, 52 + C, & 37. One of two parallel lines cuts the triangle into 2 internal triangles. The top triangle has angles, B, top, 52, right, & unknown, left. Angle, d is the exterior angle of unknown. The other triangle has angles, c, 37, & unknown.  But angle d is opposite the unknown angle. The second parallel line is at the vertex of the 37 angle along with angle, a, between the parallel line & the triangle side.  Angle 63 is the angle opposite the sum of 37 & a.Use the relationships in the diagram at right to find the values of each variable. Name which geometric relationships you used.  

 

 

Refer to the Math Notes box in Lesson 2.1.4 if you need help establishing any angle pair relationship.

Since the highlighted angles are vertical angles, and vertical angles are equal, .

is an alternate interior angle to . Recall that alternate interior angles are equal.

Use the Triangle Angle Sum Theorem to calculate : .

To find , notice that it is the exterior angle in the small triangle that contains and . What relationship do those angles have?

The diagram shows that 63 degrees is the same as 37 degrees + a.