Question

asic Geometric Shapes - Part 1 What is the value of x (3x +50) Enter your answer in the box. (6x - 10)

Answer 1

1) From the picture, we see that we have two vertical angles:

$\begin{gathered} A=(3x+50)^{\circ} \\ B=(6x-10)^{\circ} \end{gathered}$

2) Now, because of the "Vertical Angles Postulate" from geometry, we know that angles A and B are equal, so equalling the angles and replacing by their expression from above, we get the following equation in terms of x:

$\begin{gathered} A=B \\ 3x+50=6x-10 \end{gathered}$

3) We must solve the last equation for x, doing that we find:

$\begin{gathered} 3x+50=6x-10 \\ 50=6x-10-3x \\ 50+10=6x-3x \\ 60=3x \\ x=\frac{60}{3} \\ x=20 \end{gathered}$

Steps to solve the equation

0) We have the equation:

$3x+50=6x-10$

1) We want all the terms with x on one side, and the other on the other one. So we pass the term +3x to the right as -3x:

$50=6x-10-3x$

2) Now we pass the term -10 to the left as +10:

$50+10=6x-3x$

3) We sum the terms on each side:

$60=3x$

4) We pass the 3 that multiplies the x on the right, dividing the 60 on the left:

$x=\frac{60}{3}$

5) Finally we make the division and we get:

$x=20$

Answer

x = 20