Geometry Word Problem Examples - Angles

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How to solve word problems that involve geometry?

Geometry word problems involves geometric figures and angles described in words. You would need to be familiar with the formulas in geometry.
Making a sketch of the geometric figure is often helpful.

Geometry Word Problems involving Angles


In a quadrilateral two angles are equal. The third angle is equal to the sum of the two equal angles. The fourth angle is 60° less than twice the sum of the other three angles. Find the measures of the angles in the quadrilateral.


Step 1: Assign variables:

Let x = size of one of the two equal angles
Sketch the figure


Step 2: Write down the sum of angles in quadrilateral.

The sum of angles in a quadrilateral is 360°

Step 3: Plug in the values from the question and from the sketch.

360 = x + x + (x + x) + 2(x + x + x + x) – 60

Combine like terms
360 = 4x + 2(4x) – 60
360 = 4x + 8x – 60
360 = 12x – 60

Isolate variable x
12x = 420
x = 35

The question requires the values of all the angles.

Substituting x for 35, you will get: 35, 35, 70, 220

Answer: The values of the angles are 35°, 35°, 70° and 220°

Word Problems Involving Geometric Shapes, Rectangle, Triangle, Square
This video shows how to solve three word problems, each a bit more challenging, from length of a rectangle, to angles of a triangle, to finding the length of each side of a triangle that is compared to a square.

  1. The longest runway at an airport has the shape of a rectangle and an area of 1,327,700 square feet. This runway is 110 feet wide. How long is the runway?
  2. The flag of country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angles of the triangle is 35° more than three times the measure of either of the other two angles, find the measure of each angles of the triangle. (Recall that the sun of the measures of the angles of a triangle is 180°.)
  3. The perimeter of an equilateral triangle is 8 inches more that the perimeter of a square, and the side of the triangle is 5 inches longer than the side of the square. Find the side of the triangle. (Hint: An equilateral triangle has three sides the same length)

(Algebra 1) Word Problems - Geometry and Angles
Measurement and angles problem
The sum of the supplement and the complement of an angle is 130 degrees.
Find the measure of the angle.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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