7th Grade Math - Solve Simple Equations for an Unknown Angle in a Figure: CCSS.Math.Content.7.G.B.5

What angle is complement to $\frac{\pi}{6}$ ?

$\frac{\pi}{3}$

$\frac{\pi}{9}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

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

Explanation

The complement to an angle is ninety degrees subtract the angle since two angles must add up to 90. In this case, since we are given the angle in radians, we are subtracting from $\frac{\pi}{2}$ instead to find the complement. The conversion between radians and degrees is: $\pi \textup{ radians } = 180 \textup{ degrees}$

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

Reconvert the fractions to the least common denominator.

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

Reduce the fraction.

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

Calculate the area of the provided figure.

$31.5\textup{ in}^2$

$32\textup{ in}^2$

$33.5\textup{ in}^2$

$34\textup{ in}^2$

$36.5\textup{ in}^2$

Explanation

In order to solve this problem, we need to recall the area formula for a triangle:

$A=\frac{b\times h}{2}$

Now that we have the correct formula, we can substitute in our known values and solve:

$A=\frac{7\times9}{2}$

$A=31.5\textup{ in}^2$

The figure represents a set of complementary angles, solve for .

$65^\circ$

$64^\circ$

$66^\circ$

$67^\circ$

$68^\circ$

Explanation

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

Next we can solve for :

$\frac{\begin{array}[b]{r}x+25=90\ -25-25\end{array}}{x= 65}$

What is the supplementary angle to $100$^{\circ}$$ ?

$80$^{\circ}$$

$10$^{\circ}$$

$70$^{\circ}$$

$170$^{\circ}$$

$280$^{\circ}$$

Explanation

Supplementary angles add up to $180$^{\circ}$$ . In order to find the correct angle, take the known angle and subtract that from $180$^{\circ}$$ .

$180$^{\circ}$ -100$^{\circ}$ = 80$^{\circ}$$

One angle of an isosceles triangle has measure $110^{\circ }$ . What are the measures of the other two angles?

$35^{\circ },35^{\circ }$

Not enough information is given to answer this question.

$110 ^{\circ }, 40 ^{\circ }$

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

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

Explanation

An isosceles triangle not only has two sides of equal measure, it has two angles of equal measure. This means one of two things, which we examine separately:

Case 1: It has another $110^{\circ }$ angle. This is impossible, since a triangle cannot have two obtuse angles.

Case 2: Its other two angles are the ones that are of equal measure. If we let be their common measure, then, since the sum of the measures of a triangle is $180^{\circ }$ ,