Problem 1 Using the Triangle Angle-Sum Theorem
Algebra What are the values of x and y in the diagram below?
Plan
Which variable should you solve for first?
From the diagram, you know two angle measures in
| Think | Write |
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| Use the Triangle Angle-Sum Theorem to write an equation involving x. |
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| Solve for x by simplifying and then subtracting 102 from each side. |
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| Substitute 78 for
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| Solve for y by subtracting 78 from each side. |
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✓ Got It?
- Use the diagram in Problem 1. What is the value of z?
An exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side. For each exterior angle of a triangle, the two nonadjacent interior angles are its remote interior angles. In each triangle below,
The theorem below states the relationship between an exterior angle and its two remote interior angles.
Take Note: Theorem 3-11 Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
You will prove Theorem 3-11 in Exercise 33.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs