Question

work as needed. no partial credit is given for multiple choice questions. each question is worth 2 points.

1. given △sun, m∠s = 44° and m∠u = 51°. find m∠n.

(1) 39°
(2) 46°
(3) 85°
(4) 95°

1. in the accompanying diagram (l_1parallel l_2) are cut by a transversal (t). ∠4 and ∠5 can be classified as

(1) vertical angles
(2) same side interior angles
(3) corresponding angles
(4) alternate interior angles

1. in the diagram below, m∠tsv = 21° and m∠rsv = 48°. determine m∠rst.

(1) 27°
(2) 42°
(3) 69°
(4) 132°

1. given isosceles triangle abc, m∠b = 20° and (overline{ab}congoverline{ac}). which of the following choices are true?

(1) m∠a = 20° and m∠c = 140°
(2) m∠a = 140° and m∠c = 20°
(3) m∠a = 20° and m∠c = 20°
(4) m∠a = 50° and m∠c = 20°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle SUN\), we know \(m\angle S = 44^{\circ}\) and \(m\angle U=51^{\circ}\). Let \(m\angle N=x\). Then \(m\angle S + m\angle U+m\angle N = 180^{\circ}\), so \(x=180-(44 + 51)\).

Step2: Calculate \(m\angle N\)

\(x=180-(44 + 51)=180 - 95=85^{\circ}\). The answer to question 1 is (3).

Step3: Identify angle - pair relationship

When two parallel lines \(l_1\) and \(l_2\) are cut by a transversal \(T\), \(\angle4\) and \(\angle5\) are same - side interior angles. Vertical angles are opposite each other at an intersection. Corresponding angles are in the same relative position. Alternate interior angles are on opposite sides of the transversal between the parallel lines. The answer to question 2 is (2).

Step4: Use angle - addition postulate

In the diagram, \(\angle RST=\angle RSV+\angle TSV\). Given \(m\angle TSV = 21^{\circ}\) and \(m\angle RSV = 48^{\circ}\), then \(m\angle RST=21 + 48=69^{\circ}\). The answer to question 3 is (3).

Step5: Use properties of isosceles triangles

In isosceles triangle \(ABC\) with \(\overline{AB}\cong\overline{AC}\), \(\angle B=\angle C\). Given \(m\angle B = 20^{\circ}\), then \(m\angle C = 20^{\circ}\). Using the angle - sum property of a triangle (\(m\angle A+m\angle B+m\angle C = 180^{\circ}\)), we have \(m\angle A=180-(20 + 20)=140^{\circ}\). The answer to question 4 is (2).

Answer:

1. (3) \(85^{\circ}\)
2. (2) Same side interior angles
3. (3) \(69^{\circ}\)
4. (2) \(m\angle A = 140^{\circ}\) and \(m\angle C = 20^{\circ}\)