Question

use the diagram below to answer the questions on the right: 10 create a triangle angle sum equation: (a) (b) solve for x: (c) find the measure of ∠abc : (d) find the measure of ∠acb :

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So for \(\triangle ABC\), we have the equation \(x + 3x+2x=180\).

Step2: Combine like - terms

Combining the \(x\) terms on the left - hand side of the equation \(x + 3x+2x=180\), we get \(6x = 180\).

Step3: Solve for \(x\)

Dividing both sides of the equation \(6x = 180\) by 6, we have \(x=\frac{180}{6}=30\).

Step4: Find measure of \(\angle ABC\)

\(\angle ABC=x\), and since \(x = 30\), the measure of \(\angle ABC\) is \(30^{\circ}\).

Step5: Find measure of \(\angle ACB\)

\(\angle ACB = 2x\), substituting \(x = 30\), we get \(\angle ACB=2\times30 = 60^{\circ}\).

Answer:

(a) \(x + 3x+2x=180\)
(b) \(30\)
(c) \(30^{\circ}\)
(d) \(60^{\circ}\)