Question

1. emery measures the interior angles of triangle srt. which of the following are true? select two correct answers. a. ∠s is equal to 90°. b. ∠t is equal to 65°. c. ∠s is equal to 145°. d. ∠s is equal to 25°. e. ∠t is equal to 25°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In triangle SRT, we have \(\angle S=(2x + 1)^{\circ}\), \(\angle T=(5x + 5)^{\circ}\), and \(\angle R = 90^{\circ}\). So, \((2x + 1)+(5x + 5)+90=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+5x+1 + 5+90=180\), which gives \(7x+96 = 180\).

Step3: Solve for x

Subtract 96 from both sides: \(7x=180 - 96\), so \(7x=84\). Then divide both sides by 7: \(x = 12\).

Step4: Find the measure of \(\angle S\)

Substitute \(x = 12\) into the expression for \(\angle S\): \(\angle S=2x + 1=2\times12+1=24 + 1=25^{\circ}\).

Step5: Find the measure of \(\angle T\)

Substitute \(x = 12\) into the expression for \(\angle T\): \(\angle T=5x + 5=5\times12+5=60 + 5=65^{\circ}\).

Answer:

B. \(\angle T\) is equal to \(65^{\circ}\), D. \(\angle S\) is equal to \(25^{\circ}\)