Question 1

The sum of the measures of the angles of any triangle is always:

Accepted Answer

$$180^\circ$$

Question 2

If the smallest angle of a triangle is $$x$$, the middle-sized angle is $$x+36$$, and the largest angle is $$16+2x$$, what equation represents the sum of the angles in the triangle?

Accepted Answer

$$x + (x+36) + (16+2x) = 180$$

Question 3

Given the equation $$x + (x+36) + (16+2x) = 180$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 4

A triangle has angles measuring $$x$$, $$x+36$$, and $$16+2x. $$What is the measure of the largest angle?

Accepted Answer

$$80^\circ$$

Question 5

If the smallest angle in a triangle is $$32^\circ$$, and the middle-sized angle is $$36^\circ$$ more than the smallest, what is the measure of the middle-sized angle?

Accepted Answer

$$68^\circ$$

Question 6

In a triangle, the largest angle is $$16^\circ$$ more than twice the smallest angle. If the smallest angle is $$32^\circ$$, what is the measure of the largest angle?

Accepted Answer

$$80^\circ$$

Question 7

Which of the following correctly lists the measures of the three angles in the triangle described in the problem?

Accepted Answer

$$32^\circ, 68^\circ, 80^\circ$$

Question 8

If the sum of the measures of the angles in a triangle is $$180^\circ$$, and two of the angles are $$x$$ and $$x+36$$, what is the measure of the third angle in terms of $$x$$?

Accepted Answer

$$180 - (2x + 36)$$

Question 9

A triangle has angles in the ratio $$1:2:2.5. $$What are the measures of the angles?

Accepted Answer

$$32^\circ, 64^\circ, 80^\circ$$

Question 10

If the smallest angle of a triangle is $$x$$, and the largest angle is $$16$$ more than twice the smallest, which equation represents the relationship between the largest and smallest angles?

Accepted Answer

$$z = 16 + 2x$$

Question 11

A triangle has angles $$x$$, $$x+36$$, and $$16+2x. If$$ $$x is $$found to be $$32$$, what is the sum of the three angles?

Accepted Answer

$$180^\circ$$

Question 12

If the middle-sized angle of a triangle is $$36^\circ$$ more than the smallest angle, and the smallest angle is $$x$$, what is the expression for the middle-sized angle?

Accepted Answer

$$x + 36$$

Question 13

A triangle has angles $$x$$, $$x+36$$, and $$16+2x. If$$ $$x=32$$, what is the value of $$z$$?

Accepted Answer

$$80$$

Question 14

Which of the following is a correct step in solving $$x + (x+36) + (16+2x) = 180$$?

Accepted Answer

$$4x + 52 = 180$$

Question 15

If the smallest angle in a triangle is $$32^\circ$$, and the largest is $$80^\circ$$, what is the measure of the third angle?

Accepted Answer

$$68^\circ$$

Question 16

A triangle has angles $$x$$, $$x+36$$, and $$16+2x. If$$ $$x=32$$, what is the value of $$x+36$$?

Accepted Answer

$$68$$

Question 17

If the sum of the measures of the angles in a triangle is $$180^\circ$$, and the angles are $$x$$, $$x+36$$, and $$16+2x$$, what is the value of $$x$$ after simplifying the equation?

Accepted Answer

$$x = 32$$

Question 18

If a triangle has angles $$32^\circ$$, $$68^\circ$$, and $$80^\circ$$, which angle is the smallest?

Accepted Answer

$$32^\circ$$

Question 19

If the largest angle in a triangle is $$16$$ more than twice the smallest angle, and the smallest angle is $$x$$, what is the correct formula for the largest angle?

Accepted Answer

$$z = 16 + 2x$$

Solving Geometry Problems Using Algebraic Equations 3.3

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