Question

if two angles are complementary and one measures 35°, then the other
mark only one oval.
55°
65°
45°
145°

1. if two parallel lines are cut by a transversal, then alternate interior angles * 1 point

are:
mark only one oval.
supplementary
congruent
complementary
right angles

1. a triangle is translated 4 units right and 3 units up. if the original vertex is * 1 point

at (2,1), what is the new position of the vertex?
mark only one oval.
(6, 4)
(2, 4)
(6, 1)
(5, 3)

Explanation:

Step1: Recall complementary - angle definition

Complementary angles sum to 90°. Let the unknown angle be \(x\). The equation is \(x + 35^{\circ}=90^{\circ}\).

Step2: Solve for \(x\)

\(x=90^{\circ}- 35^{\circ}=55^{\circ}\)

Step3: Recall alternate - interior angles property

When two parallel lines are cut by a transversal, alternate - interior angles are congruent.

Step4: Recall translation rule

For a translation of \(a\) units right and \(b\) units up, the new coordinates \((x',y')\) of a point \((x,y)\) are given by \(x'=x + a\) and \(y'=y + b\). Here \(x = 2\), \(y = 1\), \(a = 4\), \(b = 3\). So \(x'=2 + 4=6\) and \(y'=1+3 = 4\), the new point is \((6,4)\)

Answer:

1. \(55^{\circ}\)
2. Congruent
3. \((6,4)\)