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3 years ago

How to find angles on two Line intersect

Mathematics

1 answer:

Ivan3 years ago

7 0

Hello!

Vertical angles are always congruent

This means that 3x - 35 = 130

We can solve this algebraically

3x - 35 = 130

Add 35 to both sides

3x = 165

Divide both sides by 3

x = 55

The angle AOB and AOC are supplementary which means they add to 180

First we have to find what angle AOB equals

3(55) - 35 = 130

We can subtract 180 by this number to get angle AOC

180 - 130 = 50

Angle AOC is 50

The answers are x = 55 and AOC = 50

Hope this helps!

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3 years ago

What is the equation of a line that is perpendicular to −x+3y=9 and passes through the point (−3, 2) ?

vekshin1

The equation of line that is perpendicular to the line $-x+3y =9$ and passes through the point $\left({-3,2}\right)$ is $\boxed{{\mathbf{y=-3x-7}}}$ .

Further explanation:

It is given that the equation of line is $-x+3y =9$ and passes through point $\left({-3,2}\right)$ .

Rewrite the given equation $-x+3y =9$ as follows:

$\begin{aligned}-x+3y&=9\\3y&=9+x\\y&=\frac{9}{3}+\frac{1}{3}x\\y&=\frac{1}{3}x+3\\\end{aligned}$

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It is given that both lines are perpendicular to each other so the product of slope must be equal to $-1$ .

${m_1}\cdot {m_2}=-1$ …… (1)

Substitute $\frac{1}{3}$ for ${m_1}$ in equation (1) to obtain the value of slope ${m_2}$ .

$\begin{aligned}\frac{1}{3}\cdot{m_2}&=-1\\{m_2}&=-3\\\end{aligned}$

Therefore, the slope is $-3$ .

It is given that the line passes through point $\left({-3,2}\right)$ .

The point-slope form of the equation of a line with slope $m$ passes through point $\left({{x_1},{y_1}}\right)$ is represented as follows:

$y-{y_1}=m\left({x-{x_1}}\right)$ …… (2)

Substitute $-3$ for ${x_1}$ , $2$ for ${y_1}$ and $-3$ for $m$ in equation (2) to obtain the equation of line.

$\begin{aligned}y-2&=-3\left({x-\left({-3}\right)}\right)\\y-2&=-3\left({x+3}\right)\\y&=-3x-9+2\\y&=-3x-7\\\end{aligned}$

Therefore, the equation of line is $y=-3x-7$ .

Thus, the equation of line that is perpendicular to the line $-x+3y=9$ and passes through the point $\left({-3,2}\right)$ is $\boxed{{\mathbf{y=-3x-7}}}$ .

Learn more:

1. Which classification best describes the following system of equations? brainly.com/question/9045597

2. What is the value of $x$ in the equation $x-y=30$ when $y=15$ ? brainly.com/question/3965451

3. What are the values of x? brainly.com/question/2093003

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, equation of line, line, passes through point.

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