Question

What is the value of x?

Answer 1

Hi there!

The sum of the three angles inside a triangle always equals 180°. To find the value of the third angle (called x), we first need to work out the value of the other two angles.

The first angle is given, it equals 70°.
To find the second angle (the missing interior angle), we must realise that it forms a straight angle when we add the 100° outside the triangle. A straight angle equals 180°. Turn this into an equation with the variable y, to find the answer.


`y + 100 = 180`
Subtract 100.


`y = 80`
Now we've found the second angle inside the triangle, it equals 80°.

Once more we need to set up an equation, this time in order to find the angle we're looking for: x. We use the fact that the sum of the three angles is 180°.


`80 + 70 + x = 180`
Add.


`150 + x = 180`
Subtract 150.


`x = 30`
Therefore, x equals 30°, and the answer is A.
~ Hope this helps you!

Answer 2

There is one exterior angle for the triangle that measures 100 degrees.

An exterior angle and interior angle will always add up to 180. To find this missing internal angle, set the internal and external angle to equal 180:


`100 + y = 180`

y represents the missing internal angle.

Subtract both sides by 100 to get y by itself:


`y = 80`

The missing angle will be 80.

We now have two known angles in the triangle: 70 and 80 degrees. All the interior angles of a triangle will add up to a sum of 180 degrees. Set the angles to equal 180:


`80 + 70 + x = 180`

`150 + x = 180`

Subtract both sides by 150 to get x by itself:


`\boxed{x = 30}`

The value of x will be 30.