Answer:
∠HIJ = 57
∠IJH = 57
∠JHI = 66
Step-by-step explanation:
As a much better answer to the other guy:
You first have to find what the sum of the interior angles are. This can be found using the following expression:
<em>( n - 2 ) × 180</em>
Where 'n' is the number of sides of a polygon. Since this is a triangle:
<em>n = 3</em>
Therefore, the sum the interior angles of a triangle is 180°
Returning to the triangle, it's stated that the <u>triangle is isosceles,</u> meaning the ∠HIJ is the same as the ∠IJH (the middle point notating the position of the angle.) So then you have 3 angles with the following expressions:
∠HIJ = 5x + 2
∠IJH = 5x + 2
∠JHI = 3x + 33
Since all of the angles need to add up to 180°, we can smush them all into one big equation:
5x + 2 + 5x + 2 + 3x + 33 = 180
If you simplify everything:
13x + 37 = 180
Subtract 37:
13x = 143
Divide by 13:
x = 11
Now that you have x, plug it in to the equations above!
∠HIJ = 5(11) + 2
∠IJH = 5(11) + 2
∠JHI = 3(11) + 33
Simplify.
∠HIJ = 55 + 2
∠IJH = 55 + 2
∠JHI = 33 + 33
Again.
∠HIJ = 57
∠IJH = 57
∠JHI = 66
There you go!
