Question

1. a metal beam is lifted by a forklift, as shown in the figure below. the beam creates an 83° angle with the inside of one of the tongs of the forklift. what angle is made between the beam and the other parallel tong, as indicated below?

a. 83°
b. 87°
c. 91°
d. 95°
e. 97°

1. in the figure below, lines a and b are cut by transversal line c. the 8 angles at the intersections are labeled. when true, which of the following statements cannot always be used to prove that a and b are parallel?

f. ∠1 ≅ ∠5
g. ∠2 ≅ ∠6
h. ∠2 ≅ ∠7
j. ∠3 ≅ ∠5
k. ∠4 ≅ ∠5

Explanation:

For Question 7:

Step1: Identify angle relationship

The tongs are parallel, so the unknown angle and the given \(83^\circ\) angle are same-side interior angles, which are supplementary.

Step2: Calculate unknown angle

The sum of supplementary angles is \(180^\circ\). Let the unknown angle be \(x\).
\(x = 180^\circ - 83^\circ\)

• F. \(\angle1 \cong \angle5\) are corresponding angles; congruent corresponding angles prove lines parallel.
• G. \(\angle2 \cong \angle6\) are corresponding angles; congruent corresponding angles prove lines parallel.
• H. \(\angle2 \cong \angle7\) are alternate exterior angles; congruent alternate exterior angles prove lines parallel.
• J. \(\angle3 \cong \angle5\) are alternate interior angles; congruent alternate interior angles prove lines parallel.
• K. \(\angle4 \cong \angle5\) are same-side interior angles; congruent same-side interior angles do not prove lines parallel (they need to be supplementary).

Answer:

E. \(97^\circ\)

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For Question 8: