9514 1404 393
Answer:
k = 10
Explanation:
The useful shortcut* here is that the external angle is equal to the sum of the remote internal angles.
115° = (4k+5)° +(6k+10)°
100° = 10k° . . . . . . collect terms, subtract 15°
k = 10 . . . . . . . . . . divide by 10°
_____
* I call it a shortcut because you can get there from the relations ...
- the sum of angles in a triangle is 180°
- a linear pair has a sum of 180°
If we call the internal angles X, Y, and Z, then we have ...
X + Y + Z = 180° . . . triangle sum relation
Y + 115° = 180° . . . . . linear pair relation
Equating the expressions for 180° gives ...
X + Y + Z = Y + 115°
X + Z = 115° . . . . . . . . . subtract Y from both sides