Geometry and Graphs

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GED Math › Geometry and Graphs

Questions 1 - 10

Which of the following can be the measures of the three angles of an acute isosceles triangle?

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

$32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$

$45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$

$50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$

$80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$

Explanation

For the triangle to be acute, all three angles must measure less than $90 ^{\circ }$ . We can eliminate $32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$ and $45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$ for this reason.

In an isosceles triangle, at least two angles are congruent, so we can eliminate $50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$ .

The degree measures of the three angles of a triangle must total 180, so, since $80 ^{\circ }+ 80 ^{\circ }+ 40 ^{\circ } = 200^{\circ }$ , we can eliminate $80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$ .

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$ is correct.

If the area of square is $\text{in}^2$ , what is its perimeter?

$52;\textup{in}$

$13;\textup{in}$

$26;\textup{in}$

$40;\textup{in}$

$22;\textup{in}$

Explanation

Figuring out the perimeter of a square from this information is luckily pretty easy. Since the sides of a square are all the same size, you know also that .

Taking the square root of both sides, you get:

Now, the perimeter of the square is just $4 \cdot13$ , or $52;\textup{in}$ .

Determine the area of the triangle if the base is 12 and the height is 20.

Explanation

Write the formula for the area of a triangle.

$A=\frac{BH}{2}$

Substitute the base and height into the equation.

$A=\frac{(12)(20)}{2} = 6(20) =120$

The answer is:

The image is not to scale.

If the sum of two angles results in a complementary angle, what is the measure of the unknown angle?

Capture2

$60^{\circ}$

$150^{\circ}$

$30^{\circ}$

$90^{\circ}$

$20^{\circ}$

Explanation

With the provided image, we are asked to solve for the measure of the unknown angle.

Capture2

First, we must understand some information before attempting to solve the problem. The problem provides the information that the two angles summed up result in a complimentary angle. This is another way to say that when we add the measures of the two angles, it will equal $90^{\circ}$ .

This becomes a problem where we solve for a missing variable now. We can call the unknown angle x. We would set this up in equation format accordingly:

Now, we can solve for x.

$x+30{\color{Red} -30}=90{\color{Red} -30}$

$x=60^{\circ}$

Therefore, the unknown angle is $60^{\circ}$ .

If two angles are complementary, and one angle is measured $\frac{\pi}{3}$ radians, what is the other angle in radians?

$\frac{1}{6}\pi$

$\frac{1}{3}\pi$

$\frac{1}{4}\pi$

$\frac{1}{5}\pi$

$\frac{2}{3}\pi$

Explanation

If the set of angles are complementary, they must add up to $\frac{\pi}{2}$ radians, which is equivalent to 90 degrees.

Subtract $\frac{\pi}{3}$ radians from $\frac{\pi}{2}$ radians.

$\frac{\pi}{2}-\frac{\pi}{3} = \frac{3\pi}{6}-\frac{2\pi}{6}$

The answer is: $\frac{1}{6}\pi$

Find the area of a circle with a diameter of $5\pi$ .

$\frac{25}{4}\pi^3$

$\frac{25}{4}\pi^2$

$\frac{25}{2}\pi^3$

$\frac{25}{2}\pi^2$

$\textup{The answer is not given.}$

Explanation

Write the area of a circle.

$A=\pi r^2$

The radius is half the diameter.

$r= \frac{d}{2} = \frac{5\pi}{2}$

Substitute the radius into the equation.

$A=\pi (\frac{5\pi}{2})^2=\pi (\frac{5\pi}{2})(\frac{5\pi}{2})$

The answer is: $\frac{25}{4}\pi^3$

If the circumference of a circle is , what is the area of the circle in square inches? Use $\pi=3.14$ .

Explanation

Recall how to find the circumference of a circle.

$\text{Circumference}=2\pi r$ , where is the radius.

Plug in the given circumference and solve for the radius.

$50.24=2\pi r$

Next, recall how to find the area of a circle.

$\text{Area}=\pi r^2$

Plug in the given radius to find the area.

$\text{Area}=(3.14)(8)^2=200.96$

Suppose two angles are complementary. If one angle measurement is 52 degrees, what is the other angle?

Explanation

Complementary angles sum up to 90 degrees.

Subtract the known angle from 90.

The answer is:

Find the area of a square with a side of .

Explanation

Write the formula for the area of a square.

Substitute the side.

The answer is:

If two angles are complementary, and one angle is $75^{\circ}$ , what is the value of the other angle?

$15^{\circ}$

$105^{\circ}$

$30^{\circ}$

$285^{\circ}$

$150^{\circ}$

Explanation

Two angles are complementary if they add up to $90^{\circ}$ . We can use the formula:

$x+y=90^{\circ}$

where x and y are the angles.

Now, we know one angle is $75^{\circ}$ . So, we will substitute and solve for the other angle. We get

$x+75^{\circ}=90^{\circ}$

$x+75^{\circ}-75^{\circ}=90^{\circ}-75^{\circ}$

$x+0^{\circ} = 15^{\circ}$

$x=15^{\circ}$

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