Question

Can anyone help me on this? I need an exact answer please no guesses

Answer 1

x = 32°

The triangle has 2 equal sides and is therefore isosceles, thus the 2 base angles are also congruent.

The 2 base angles are of size x°

x =
`(180 - 116)/(2)` =
`(64)/(2)` = 32

Answer 2

This is an isosceles triangle (meaning two sides have equal lengths).

If the sides are equal, then their corresponding angles are congruent (equal).

Let's call the unlabeled angle "y".

side length 17 has corresponding angle 116°

side length 10 has corresponding angle x°

the other side length 10 has corresponding angle y°

since the side lengths of 10 correspond to angle x and angle y, then ∠x = ∠y.

NEXT, the sum of the angles of a triangle = 180°

∠x + ∠y + 116° = 180°

∠x + ∠x + 116° = 180° substituted ∠y with ∠x since they are congruent

2(∠x) + 116° = 180° simplified (added like terms)

2(∠x) = 64° subtracted 116° from both sides

∠x = 32° divided both sides by 2

Answer: x = 32°