Solve for Unknown Angles — Angles in a Triangle

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New York State Common Core Math Geometry, Module 1, Lesson 8

Worksheets for Geometry

Student Outcomes

  • Students review formerly learned geometry facts and practice citing the geometric justifications regarding angles in a triangle in anticipation of unknown angle proofs.

Solve for Unknown Angles — Angles in a Triangle


Opening Exercise

Find the measure of angle 𝑥 in the figure to the right. Explain your calculations. (Hint: Draw an auxiliary line segment.)


The sum of the 3 angle measures of any triangle is ______.

INTERIOR OF A TRIANGLE: A point lies in the interior of a triangle if it lies in the interior of each of the angles of the triangle.

In any triangle, the measure of the exterior angle is equal to the sum of the measures of the ____ angles. These are sometimes also known as ____ angles. Base angles of an ____ triangle are equal in measure. Each angle of an ____ triangle has a measure equal to 60°.

Relevant Vocabulary

ISOSCELES TRIANGLE: An isosceles triangle is a triangle with at least two sides of equal length.

ANGLES OF A TRIANGLE: Every triangle △ 𝐴𝐵𝐶 determines three angles, namely, ∠𝐵𝐴𝐶, ∠𝐴𝐵𝐶, and ∠𝐴𝐶𝐵. These are called the angles of △ 𝐴𝐵𝐶.

EXTERIOR ANGLE OF A TRIANGLE: Let ∠𝐴𝐵𝐶 be an interior angle of a triangle △ 𝐴𝐵𝐶, and let 𝐷 be a point on ⃡𝐴𝐵 such that 𝐵 is between 𝐴 and 𝐷. Then ∠𝐶𝐵𝐷 is an exterior angle of the triangle △ 𝐴𝐵𝐶.

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