Question

Can anyone help me with these questions 4. Find the values of x and yA. O x = 12, y = 54B. O x = 12, y = 108 C. O x = 36, y = 54 D. O x = 36, y = 108

Answer 1

Both triangles in the picture share one vertex, their sides form an X shape. The angles that share that vertex are vertically opposite angles, which indicates that they are congruent.

Then we can conclude that

`y=108`

Both red marks in the base angles of the lower triangle indicate that both angles are equal.

The sum of the inner angles of a triangle is 180º, we know the measure of one of the angles and the other two are congruent, we can determine the following expression:

`3x+3x+108=180`

From this expression, we can determine the value of x, first step is to simplify the like terms:

`6x+108=180`

Next, pass 108 to the right side of the equation by applying the opposite operation to both sides of it:

`\begin{gathered} 6x+108-108=180-108 \\ 6x=72 \end{gathered}`

Finally, divide both sides by 6 to reach the value of x:

`\begin{gathered} (6x)/(6)=(72)/(6) \\ x=12 \end{gathered}`

The values of x and y are:

`x=12º\text{ and y=108º}`

Correct choice is B.