Question

The measures of the angles in a triangle are x, 2x, and 3x. The triangle is

acute
right
obtuse

Answer 1

Right.

Explanation:

According to the types of angles there are three types of triangle,

1) Acute triangle : a triangle with three acute angles (less than 90°)

2) Obtuse triangle : a triangle which having one obtuse angle (greater than 90°) and two acute angles.

3) Right triangle : a triangle which having one right angle and two acute angles.

Given,

The measures of the angles in a triangle are x, 2x, and 3x.

We know that the sum of all 3 interior angles of a triangle is supplementary,

⇒ x + 2x + 3x = 180° ⇒ 6x = 180° ⇒ x = 30°,

Hence, the measurement of the angles in the given triangle are,

30°, (2×30)°, (3×30)°

= 30°, 60°, 90°

Thus, by the above definitions,

Given triangle is right.

Answer 2

we know that

The triangle is acute if the larger angle is less than
`90` degrees

The triangle is right if the larger angle is equal to
`90` degrees

The triangle is obtuse if the larger angle is greater than
`90` degrees

Remember that

The sum of the internal angles of a triangle is equal to
`180` degrees

so

In this problem

`x+2x+3x=180\°`

Solve for x

`6x=180\°`

`x=30\°`

The angles of the triangle are

`30\°-60\°-90\°`

The larger angle is equal to
`90` degrees

therefore

the answer is

right