Multi-Step Angle Problems Worksheets Grade 7

Geometry

Angle Calculations

Each printable worksheet below is a full page of practice problems and comes with an answer key that explains how to solve every problem, step by step. Open a worksheet and use the Print / Save as PDF button to download it.

Worksheet 1

8 problems
  1. Aroha is designing a kite. The kite is shaped like a quadrilateral with one pair of parallel sides. Two angles of the kite are given: one angle measures 7x + 15 degrees, and the other angle (adjacent to it on the same parallel side) measures 3x + 25 degrees. These two angles are supplementary. What is the measure of each of these two angles?
  2. Isabella is designing a triangular sail for a model boat. The sail is a right triangle. One of the acute angles measures 4 times the measure of the other acute angle. What are the measures of the two acute angles?
  3. Liam is designing a triangular garden with angles that have a ratio of 2:3:4. He needs to determine the measure of the largest angle to ensure proper sunlight exposure for his plants. What is the measure of the largest angle in degrees?

…and 5 more problems

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Worksheet 2

8 problems
  1. Liam is designing a triangular garden plot with angles that form an arithmetic sequence. The smallest angle is 30 degrees. What are the measures of all three angles in his garden plot?
  2. Two supplementary angles have measures (7x + 12)° and (5x + 18)°. Find the value of x.
  3. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (12, 1), (12, 8), and (2, 8). A diagonal path is drawn from (2, 1) to (12, 8), dividing the garden into two triangular sections. What is the area of one of these triangular sections?

…and 5 more problems

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Worksheet 3

8 problems
  1. Hana is designing a triangular sail for her model boat. She draws a diagram of a right triangle where one acute angle is twice the measure of the other acute angle. The smallest angle of the triangle is labeled x. Find the measure of each angle in the triangle.
  2. Emma is designing a triangular patio with sides measuring 18 feet, 24 feet, and 30 feet. She wants to create a similar triangular flower bed where the shortest side is only 12 feet. What will be the perimeter of the smaller flower bed?
  3. In triangle ABC, angle A = 2x, angle B = 3x, and angle C = 4x. Find the value of x and the measure of each angle.

…and 5 more problems

Open & Print Worksheet 3

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