Question
Triangle Angle Sum Theorem Quick Check
4 of 54 of 5 Items
Question
The angles of a triangle measure (x+10)°
, (x+20)°
, and (x+30)°
. Find the measure of the smallest angle.(1 point)
Responses
70°
70 degrees
60°
60 degrees
40°
40 degrees
50°
50 degrees
Skip to navigation
page 12 of 12
Answers
GPT-4o mini
To solve for the smallest angle in the triangle, we first need to find the value of \(x\) using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle equals 180°.
The angles are given as:
- Angle 1: \((x + 10)^\circ\)
- Angle 2: \((x + 20)^\circ\)
- Angle 3: \((x + 30)^\circ\)
We can set up the equation like this:
\[
(x + 10) + (x + 20) + (x + 30) = 180
\]
Combining like terms gives us:
\[
3x + 60 = 180
\]
Next, we solve for \(x\) by subtracting 60 from both sides:
\[
3x = 120
\]
Now, divide by 3:
\[
x = 40
\]
Now we can find the measures of the angles:
- Angle 1: \(x + 10 = 40 + 10 = 50^\circ\)
- Angle 2: \(x + 20 = 40 + 20 = 60^\circ\)
- Angle 3: \(x + 30 = 40 + 30 = 70^\circ\)
The angles of the triangle are \(50^\circ\), \(60^\circ\), and \(70^\circ\).
Thus, the smallest angle is:
\[
\boxed{50^\circ}
\]
The angles are given as:
- Angle 1: \((x + 10)^\circ\)
- Angle 2: \((x + 20)^\circ\)
- Angle 3: \((x + 30)^\circ\)
We can set up the equation like this:
\[
(x + 10) + (x + 20) + (x + 30) = 180
\]
Combining like terms gives us:
\[
3x + 60 = 180
\]
Next, we solve for \(x\) by subtracting 60 from both sides:
\[
3x = 120
\]
Now, divide by 3:
\[
x = 40
\]
Now we can find the measures of the angles:
- Angle 1: \(x + 10 = 40 + 10 = 50^\circ\)
- Angle 2: \(x + 20 = 40 + 20 = 60^\circ\)
- Angle 3: \(x + 30 = 40 + 30 = 70^\circ\)
The angles of the triangle are \(50^\circ\), \(60^\circ\), and \(70^\circ\).
Thus, the smallest angle is:
\[
\boxed{50^\circ}
\]