Question

Find the value of x. please.

Answer 1

Let's look at the image and think about it for a second. We are given an exterior angle, and two opposite interior angles.

The sum of all angles in a triangle are equal to 180˚. If we look at angle ∠x , we notice something: it is a supplementary angle! ∠x + its supplementary angle is equivalent to 180. Conveniently enough, this supplementary angle is also an interior angle of the triangle.

You might be thinking, "Okay, so ∠x is a supplementary angle. Cool, so what?" Allow me to explain. Let's represent the unknown interior angle inside the triangle as 'n' (this isn't necessary to solve for x, but I'm just trying to prove how the solution works so you'll understand how to do these)

∠x + ∠n = 180˚ (These angles are supplementary)

∠n + 59˚ + 71˚ = 180˚ (The sum of interior angles of a triangle is 180˚)

If we isolate ∠n in both equations, then:

∠n = 180˚ - ∠x

∠n = 180˚ - 59˚ - 71˚

Since the right sides of both equations are equal, we can turn it into a single equation:

∠n = ∠n

180˚ - ∠x = 180˚ - 59˚ - 71˚

Isolate ∠x:

∠x = 59˚ + 71˚

So, what does this mean? This proof, essentially, establishes the fact that an exterior angle is equivalent to the sum of the two opposite interior angles. As you can see with the proof we made, ∠x is equal to the two opposite angles in the triangle, 59˚ and 71˚.

Now, let's get ourselves a definitive answer:

∠x = (59˚ + 71˚)

∠x = 130˚

If you have any further questions on how I got to the answer, just ask in the comments! Good luck!

- breezyツ

Answer 2

Answer:

130°

Step-by-step explanation:

1. 59 + 71 (We do this because we want to find out their total to help us find out what the angle next to x is)

2. This should have given you 130°. Then, we will subtract 130 from 180 (180-130) (We do this because angles in a triangle add up to 180, so we want to find out what the single angle is).

3. This should have given you 50°. Since we know that angles on a straight line add up to 180°, we subtract 50 from 180 (180-50), and will eventually end up with 130°, so x=130°.