Question

spaced review
1 determine the supplement of each angle measure.
(a) 63°
(b) 10°
(c) 180°
2 determine the complement of each angle measure.
(a) 10°
(b) 75°
(c) 45°
3 the length of the legs of a right - triangle are 6 in. and 8 in. use the pythagorean theorem to determine the length of the hypotenuse. show your work.
4 solve for b in the equation $\frac{a - b}{12}=11 - 6a$.
5 list the properties that are shared by each pair of polygons.
(a) squares and equilateral triangles
(b) rectangles and rhombi
6 list three different properties of a square.
7 identify the vertical angles.
8 identify the pairs of angles. describe the measures of the angles in each pair.

Explanation:

1.

Step1: Recall supplement - angle formula

The supplement of an angle $\theta$ is $180^{\circ}-\theta$.

a.

$180 - 63=117^{\circ}$

b.

$180 - 10 = 170^{\circ}$

c.

$180-180 = 0^{\circ}$

Step1: Recall complement - angle formula

The complement of an angle $\theta$ is $90^{\circ}-\theta$.

a.

$90 - 10=80^{\circ}$

b.

$90 - 75 = 15^{\circ}$

c.

$90 - 45=45^{\circ}$

Step1: Recall Pythagorean theorem

For a right - triangle with legs $a$ and $b$ and hypotenuse $c$, $c^{2}=a^{2}+b^{2}$. Here $a = 6$ in and $b = 8$ in.

Step2: Calculate $c^{2}$

$c^{2}=6^{2}+8^{2}=36 + 64=100$

Step3: Find $c$

$c=\sqrt{100}=10$ in

Answer:

a. $117^{\circ}$
b. $170^{\circ}$
c. $0^{\circ}$

2.