The angles of a triangle measure (x+10)°

Question

, (x+20)°
, and (x+30)°
. Find the measure of the smallest angle.(1 point)
Responses

50°
50 degrees

60°
60 degrees

40°
40 degrees

70°

Answer 1

To find the measure of the smallest angle in the triangle, we start by using the fact that the sum of the angles in a triangle is always 180 degrees.

The angles of the triangle are given as:

• Angle 1: \( (x + 10)^\circ \)
• Angle 2: \( (x + 20)^\circ \)
• Angle 3: \( (x + 30)^\circ \)

We can set up the equation: \[ (x + 10) + (x + 20) + (x + 30) = 180 \]

Combining the terms gives: \[ 3x + 60 = 180 \]

Next, we solve for \( x \): \[ 3x = 180 - 60 \] \[ 3x = 120 \] \[ x = 40 \]

Now, we can find the measures of the angles:

1. \( (x + 10) = (40 + 10) = 50^\circ \)
2. \( (x + 20) = (40 + 20) = 60^\circ \)
3. \( (x + 30) = (40 + 30) = 70^\circ \)

The measures of the angles are 50°, 60°, and 70°.

Thus, the smallest angle is: 50°