Question

1.

Answer 1

The correct answer for Number 1 is

A.

$EXPLANATION$

First we apply the vertical angles theorem to transfer x into the triangle. That is,

$x=y$

Next, we use the triangle angle sum theorem to write an equation in x, which is

$x+70+30=180$

We can solve this equation for x.

Part B

We now solve the equation to obtain,

$x+100=180$

$x=180-100$

This gives us,

$x=80$

and

$y=80$

The correct answer for this part is B.

2)

By the triangle exterior angle theorem,



The correct answer for this part is D.

3) The correct answer is the Triangle exterior angle theorem.

This theorem says that the sum of any two adjacent interior angles of a triangle equals the exterior angle opposite to them.

4) Using the triangle angle sum theorem, we can solve for x.

So we are adding all the angles in the triangle and equate them to 180.

$(2x+4)+(2x-9)+x=180$

We group like terms to obtain,

$2x+2x+x=180+9-4$

This simplifies to,

$5x=185$

we divide both sides by 5 to get,

$x=\frac{185}{5}=37$

The correct answer for this question 4 is C