Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryEasy
A surveyor measures the angles of a quadrilateral. Three of the angles are 85°, 110°, and 70°. What is the measure of the fourth angle?
- A100°
- B95°
- C85°
- D90°
Show answer & explanationAnswer & explanation
Correct answer: B. 95°
The sum of the interior angles of any quadrilateral is always 360°. Given three angles are 85°, 110°, and 70°, their sum is 85 + 110 + 70 = 265°. To find the fourth angle, subtract this sum from 360°: 360° - 265° = 95°.
Why the other options are wrong
- A. This value would make the sum of angles greater than 360 degrees.
- C. This value would make the sum of angles less than 360 degrees.
- D. This would mean the quadrilateral is a rectangle or has a right angle, but the sum would be off.
Sum of Angles in a Quadrilateral
The total measure of all interior angles within any four-sided polygon (quadrilateral).
- The sum of interior angles in any quadrilateral is always 360 degrees.
- This property applies to squares, rectangles, parallelograms, trapezoids, etc.
- Can be used to find an unknown angle if the others are known.
Memory trick: N minus two, times one-eighty, for any polygon's angle sum, it's weighty!