Question

question 10/25
solve for x:
use the diagram below to answer the questions on the right:
30
(c)
find the measure of ∠abc:
30
(d)
find the measure of ∠acb:
60
(e)
find the measure of ∠bac:

Explanation:

Step1: Use angle - sum property of a triangle

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

Step2: Combine like - terms

Combining the \(x\) terms on the left - hand side gives \(6x = 180\).

Step3: Solve for \(x\)

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

Step4: Find \(\angle ABC\)

Since \(\angle ABC=x\) and \(x = 30\), then \(\angle ABC = 30^{\circ}\).

Step5: Find \(\angle ACB\)

Since \(\angle ACB = 2x\) and \(x = 30\), then \(\angle ACB=2\times30 = 60^{\circ}\).

Step6: Find \(\angle BAC\)

Since \(\angle BAC = 3x\) and \(x = 30\), then \(\angle BAC=3\times30 = 90^{\circ}\).

Answer:

Solve for \(x\): \(30\)
(c) Measure of \(\angle ABC\): \(30^{\circ}\)
(d) Measure of \(\angle ACB\): \(60^{\circ}\)
(e) Measure of \(\angle BAC\): \(90^{\circ}\)