Question

In ΔMNO,

m
∠
M
=
(
6
x
+
1
)
∘
m∠M=(6x+1)
∘
,
m
∠
N
=
(
3
x
−
10
)
∘
m∠N=(3x−10)
∘
, and
m
∠
O
=
(
x
+
19
)
∘
m∠O=(x+19)
∘
. Find
m
∠
N
.
m∠N.

Answer 1

Explanation:

All the angles in a triangle add up to 180°

So you need to add up all your angles and set them equal to 180°

angleM + angleN + angleO=180

(6x+1) + (3x-10) + (x+19)= 180

We don't actually need all these parentheses; this is all just addition and subtraction.

6x+1+3x-10+x+19 =180

Add all the x terms together. Add all the constants (plain numbers) together.

10x + 10 =180

Subtract 10 from both sides

10x =170

Divide by 10.

x = 17

But you need one more step because if you reread the question, you are being asked for the measure of angle N, which is 3x - 10

3*17 - 10 =

51 - 10 =

41

The measure of angle N is 41°