42.9k views
3 votes
Find m/KMN. L 60° K 1⁰40 6x (11x+15)° N​

Find m/KMN. L 60° K 1⁰40 6x (11x+15)° N​-example-1

2 Answers

6 votes

Answer:

the answer is angle 90

Explanation:

User Nikolay Tsonev
by
8.2k points
2 votes

Answer:

114°

Explanation:

The exterior angle is the sum of the remote interior angles.

__

setup

(11x +15)° = 60° +6x°

solution

5x = 45 . . . . . . . . . divide by °, subtract 15+6x

x = 9 . . . . . . . . . . divide by 5

The measure of exterior angle KMN is ...

m∠KMN = (11(9) +15)° = 114°

_____

Additional comment

Both the sum of interior angles and the sum of angles of a linear pair are 180°. If M represents the interior angle at vertex M, then we have ...

60° +6x° +M = 180°

(11x +15)° +M = 180°

Equating these expressions for 180° and subtracting M gives the relation we used above:

(11x +15)° +M = 60° +6x° +M . . . . . equate the two expressions for 180°

(11x +15)° = 60° +6x° . . . . . . . . . . . subtract M

This is also described by "supplements to the same angle are equal."

User Carlosveucv
by
8.6k points

Related questions

asked Jul 1, 2024 82.1k views
Ed Knowles asked Jul 1, 2024
by Ed Knowles
7.7k points
1 answer
2 votes
82.1k views
asked Jun 27, 2024 136k views
Germmand asked Jun 27, 2024
by Germmand
8.0k points
1 answer
0 votes
136k views