The measures of three angles of a triangle are given (8x-5)°, (2x)°, and (3x-10)°. what is the measure of the largest angle?

You have three angles,

we know that the some of the three angles of a triangle is 180 degrees,

then
(
8
x
−
5
)
+
(
2
x
)
+
(
3
x
−
10
)
=
180
, (1)

solve the eq. (1),

8
x
−
5
+
2
x
+
3
x
−
10
=
180
8
x
+
2
x
+
3
x
−
5
−
10
=
18
13
x
−
15
=
180
13
x
=
180
+
15
13
x
=
195
x
=
195
13
x
=
15
then we have to substitute the value of x = 15 in each expression of the angles
8
x
−
5
=
8
⋅
15
−
5
8
x
−
5
=
120
−
5
8
x
−
5
=
115
2
x
=
2
⋅
15
=
30
3
x
−
10
=
3
⋅
15
−
10
=
45
−
10
=
35
So the largest angle is (8x-5)