Question

the angles of a triangle are the following:
m∠1 = 4x + 12
m∠2 = 6x − 3
m∠3 = 3x + 2
what is the measure of each of the angles?

answer

angle 1 =
angle 2 =
angle 3 =

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\), so \((4x + 12)+(6x - 3)+(3x + 2)=180\).

Step2: Combine like terms

\(4x+6x+3x + 12-3 + 2 = 180\) simplifies to \(13x + 11 = 180\).

Step3: Solve for \(x\)

Subtract 11: \(13x=180 - 11 = 169\), then \(x=\frac{169}{13}=13\).

Step4: Find each angle

• Angle 1: \(4(13)+12 = 52 + 12 = 64\)
• Angle 2: \(6(13)-3 = 78 - 3 = 75\)
• Angle 3: \(3(13)+2 = 39 + 2 = 41\)

Answer:

Angle 1 = \(64^\circ\)
Angle 2 = \(75^\circ\)
Angle 3 = \(41^\circ\)