Geometry Word Problem Examples - Angles

Geometry Word Problems involving Angles

Angle word problems using algebra involve setting up and solving equations based on the properties of angles. These problems often include relationships such as complementary angles, supplementary angles, vertical angles, or angles in geometric shapes like triangles and polygons.

How to solve word problems that involve angles?

Key Tips for Angle Problems:

1. Draw a diagram: This is extremely helpful to visualize the angles and their relationships.
2. Know your angle relationships: Complementary (add to 90°), supplementary (add to 180°), vertical angles (equal), angles on a line (add to 180°), angles in a triangle (add to 180°), angles in a quadrilateral (add to 360°).
3. Define variables: Use variables to represent unknown angles.
4. Write an equation: Translate the word problem into an algebraic equation.
5. Solve for the variables: Use algebraic techniques to solve for the unknown angles.
6. Check your answer: Make sure your answer makes sense in the context of the problem. Do the angles add up correctly? Are the relationships satisfied?

The following diagram gives the steps to solve an angle word problem using Algebra.

Geometry Word Problems
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Angle Word Problems

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Here are some examples of angle word problems using algebra, along with step-by-step solutions:

Example:
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.

Solution:
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.
Example:

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)
   

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

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