Question

Find the value of x . WILL GIVE 100 POINTS!

Answer 1

• x = 105°

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x is the exterior angle of the triangle.

Exterior angle is the sum of remote interior angles:

• x = 55° + 50°
• x = 105°

Answer 2

`x\textdegree = 105\textdegree`

Explanation:

To find x, we must first find its corresponding interior angle.

We know that the measures of the interior angles of a triangle add to 180°.

From this, we can construct an equation for x's corresponding interior angle, which I will label y.

`y \textdegree + 55\textdegree + 50\textdegree = 180\textdegree`

Then, we can solve for y by subtracting 55° and 50° from both sides.

`y\textdegree = 180\textdegree - 55\textdegree - 50\textdegree`

`y\textdegree = 125\textdegree - 50\textdegree`

`y\textdegree = 75\textdegree`

Now, we can solve for x, as any interior angle of a triangle and its corresponding exterior angle are supplementary; their measures add to 180°.

`x\textdegree + y\textdegree = 180\textdegree`

`x\textdegree + 75\textdegree = 180\textdegree`

`x\textdegree = 105\textdegree`