The formula for the sum of interior angles for a polygon is
where s is the number of sides of the polygon.
In the first practice question, you’re asked to find the missing interior angle in a quadrilateral. The second question gets a little trickier, because it also tests your knowledge of isosceles triangles as well as vertical angles.
Practice questions
Refer to this diagram to answer the following question.
- What is the value of k in the diagram?
A. 15 B. 105 C. 285 D. 35 E. 75
- What is the value of n in the following diagram?
A. 80 B. 140 C. 120 D. 65 E. 40
Answers and explanations
- The correct answer is Choice (E).
The sum of the interior angle measures of a quadrilateral (four-sided polygon) is 360 degrees. Therefore, the sum of 108, 101, 76, and k is 360. You can set up an equation and solve for k.
- The correct answer is Choice (E).
If two sides of a triangle are congruent, the angles opposite those sides are congruent. Therefore, the two triangle angles that aren’t labeled with measures have the same measure. Their sum must be 80 degrees, because the sum of the interior angles of the triangle is 180 degrees and the labeled angle is 100 degrees:
180 – 100 = 80
Because the sum of the two angles is 80 degrees and the two angles have the same measure, each one has to be 40 degrees. One of them is a vertical angle to the n-degree angle, and vertical angles are congruent, so the n-degree angle is also 40 degrees. Therefore, the value of n is 40.