The measures of the angles of a triangle can be represented by the expressions x degrees, quantity of x plus twenty degrees, and two times x degrees. Which word best describes the triangle?

The triangle is an acute triangle.

The triangle is a right triangle.

The triangle is an obtuse triangle.

There is not enough information to classify the triangle.

Question

The measures of the angles of a triangle can be represented by the expressions x degrees, quantity of x plus twenty degrees, and two times x degrees. Which word best describes the triangle?

The triangle is an acute triangle.

The triangle is a right triangle.

The triangle is an obtuse triangle.

There is not enough information to classify the triangle.

anonymous · Answer

Remember that the degrees in a triangle equal to 180 degrees (so this would be represented as Angle  1 + Angle 2 + Angle 3 = 180). In this question, each angle is represented by three different expressions: x, x+20, and 2x. To find the solution for your question, you must first solve for x: 

$$x+(x+20)+2x=180$$
$$4x+20=160$$
$$x=40$$

Then plug in the value of x into each expression (x, x+20, and 2x). You'll find that the angles equal 40, 60, and 80 correspondingly. Which tells you that the triangle is an ACUTE triangle.