MEASURING ANGLES OF TRIANGLES WORKSHEET

Find the Angle Measures of Triangle Using Ratios

Problem 1 :

The ratio of the angle measures of a triangle is 1: 1: 1. Find the angle measures. Then classify the triangle by its angle measures.

Solution

Problem 2 :

The ratio of the angle measures in a triangle is 6 : 5 : 4. Find the angle measures. Then classify the triangle by its angle measures.

Solution

Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

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Problem 8 :

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Problem 9 :

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Problem 10 :

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Problem 11 :

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Problem 12 :

Find the value of x.

Solution

Problem 13 :

The ratio of the interior angle measures of a triangle is 2 : 3 : 5. What are the angle measures?

Solution

Problem 1 :

If the perimeter of the given triangle is 49 inches, find the missing side.

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Problem 2 :

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Problem 3 :

Solution

Problem 4 :

The perimeter of a triangle is 29 millimeters. The length of the first side is twice the length of the second side. The length of the third side is 5 more than the length of the second side. Find the side lengths of the triangle. Then classify the triangle by its side lengths.

Solution

Problem 5 :

The perimeter of a triangular window is 141 inches. The ratio of the side lengths of the window is 11 : 18 :18. Draw and label a diagram of the window. What are the side lengths of the window? Classify the window by its side lengths.

Solution

Problem 6 :

The ratio of the angle measures of a triangle is 7 : 16 : 22. Find the angle measures. Then classify the triangle by its angle measures.

Solution

Problem 7 :

The ratio of the side lengths of a triangle is 7 : 24 : 25. The perimeter of the triangle is 392 inches.

a) Find the side lengths. Then classify the triangle by its side lengths.

b) is the triangle a right triangle ? How do you know?

Solution

Problem 8 :

Two sides of a triangle are 12 cm and 14 cm. If the perimeter of the triangle is 36 cm, find the third side.

Solution

Problem 1 :

In the accompanying diagram of triangle BCD, triangle ABC is an equilateral triangle and AD = AB. What is the value of x, in degrees?

Solution

Problem 2 :

The measure of the vertex angle of an isosceles triangle is 15 more than the measure of each base angle. Find the  degrees in each angle of the triangle.

Solution

Problem 3 :

The measure of each base angle of an isosceles triangle is seven times the measure of the vertex angle. Find the measure of each angle.

Solution

Problem 4 :

The measure of each of the congruent angles of an isosceles triangle is 9 degree less than 4 times the vertex angle. Find the measure of each angle of the triangle.

Solution

Problem 5 :

If

∠1 = 4x - 3y

∠2 = 3x - 5y

∠3 = 204 - 15x + 16y and ∠4 = 6x - 18

Find x and y.

Solution

Problem 6 :

In the figure, triangle ABC is ≅ triangle FDE

i) Find the value of x 

ii) Find the value of y.

Solution

Problem 7 :

In a triangle the measure of the second angle is 3 times the measure of the first angle, and the measure of the third angle is 5 times the measure of the first angle. Find the measure of each angle.

Solution

Problem 8 :

In a right triangle ABC, angle A and angle B are acute angles, the measure of ∠B is 24 less than the measure of ∠A. Find ∠A and ∠B.

Solution

Problem 9 :

The second angle of a triangle is 2° less than three times the measure of the first angle. The third angle of a triangle is 14° more than two times the first angle. Determine the measure of the smallest angle.

Solution

Problem 10 :

In a triangle, the second angle is 25° larger than the first angle. The third angle is three times the measure of the first angle. Determine the measure of the largest angle.

Solution