Applying the Angle Theorems (Geometry)
Free printable Geometry geometry worksheet: apply the vertical angles, parallel lines, triangle angle sum, and isosceles base angles theorems to find missing angle measures.
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Geometry · Math worksheet
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Applying the Angle Theorems
Use the Vertical Angles Theorem, the parallel-lines-and-transversal theorems, the Triangle Angle Sum Theorem, and the Isosceles Triangle Base Angles Theorem to find each missing angle.
- 1.Two lines intersect, forming two pairs of vertical angles. One angle measures 124°. Use the Vertical Angles Theorem to find the measure of the angle vertically opposite it.
- 2.Two lines intersect, forming two pairs of vertical angles. One angle measures 132°. Use the Linear Pair Postulate to find the measure of an angle adjacent to it.
- 3.Two lines intersect, forming two pairs of vertical angles. One angle measures 106°. Use the Vertical Angles Theorem to find the measure of the angle vertically opposite it.
- 4.Two parallel lines are cut by a transversal. One interior angle measures 72°. Use the Alternate Interior Angles Theorem to find the measure of its alternate interior angle.
- 5.Two parallel lines are cut by a transversal. One angle measures 143°. Use the Corresponding Angles Postulate to find the measure of its corresponding angle at the other intersection.
- 6.Two parallel lines are cut by a transversal. One interior angle measures 118°. Use the Alternate Interior Angles Theorem to find the measure of its alternate interior angle.
- 7.A triangle has interior angles of 39° and 25°. Use the Triangle Angle Sum Theorem to find the third angle.
- 8.A triangle has interior angles of 52° and 74°. Use the Triangle Angle Sum Theorem to find the third angle.
- 9.A triangle has interior angles of 70° and 37°. Use the Triangle Angle Sum Theorem to find the third angle.
- 10.An isosceles triangle has a vertex (apex) angle of 40°. Use the Isosceles Triangle Base Angles Theorem and the Triangle Angle Sum Theorem to find each base angle.
- 11.An isosceles triangle has a base angle of 33°. Use the Isosceles Triangle Base Angles Theorem and the Triangle Angle Sum Theorem to find the other base angle and the vertex (apex) angle.
- 12.An isosceles triangle has a vertex (apex) angle of 82°. Use the Isosceles Triangle Base Angles Theorem and the Triangle Angle Sum Theorem to find each base angle.
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