Question

1. (l30) find the measures of the angles of a triangle whose angles have measures of x - 20, 3x, and 4x.

a. 35, 55, 90
b. 5, 40, 65
c. 15, 25, 45
d. 5, 75, 100
e. none of the above

1. (l28) a polygon is a geometric figure whose sides are

a. lines
b. line segments

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x - 20)+3x + 4x=180\).

Step2: Combine like terms

Combine the \(x\) terms: \((1 + 3+4)x-20 = 180\), which simplifies to \(8x-20 = 180\).

Step3: Solve for \(x\)

Add \(20\) to both sides: \(8x=180 + 20\), so \(8x=200\). Then divide both sides by \(8\): \(x=\frac{200}{8}=25\).

Step4: Find \(4x\)

Substitute \(x = 25\) into \(4x\): \(4\times25 = 100\).

Answer:

D. \(5,75,100\)