Question

In ΔHIJ,

m
∠
H
=
(
4
x
+
1
)
∘
m∠H=(4x+1)
∘
,
m
∠
I
=
(
2
x
−
6
)
∘
m∠I=(2x−6)
∘
, and
m
∠
J
=
(
6
x
−
7
)
∘
m∠J=(6x−7)
∘
. Find
m
∠
J
.
m∠J.

Answer 1

89 degrees

Explanation:

Since these angles make up a triangle, we know that the total of these angles will make 180 degrees. So, we need to set the equations up appropriately, and solve for x:

`180=(4x+1)+(2x-6)+(6x-7)\\180=12x-12\\192=12x\\x=16\\`

Then, you plug 16 back into the equation for angle J, and simplify:

`(6(16)-7)\\(96-7)\\(89)`

Therefore, the answer is 89 degrees.