What is the value of k? (picture attached)

Answer: k= 10

Explanation:

? + 115= 180
180-115=65

the unknown interior angle is 65 degrees since they’re supplementary angles

every triangle has an interior angle total of 180 degrees. since we have the 65 degree angle known, the others can be solved.

180-65= 115
(4k+5)+(6k+10)= 115
10k+15= 115
-15 -15
10k= 100
k=10

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Alleei Alleei · Answer 2 · 2020-04-01T12:50:55+02:00

Answer : The value of 'k' is, [tex]10^o[/tex]

Step-by-step explanation :

As we know that, the exterior angle of a triangle is equal to the sum of opposite two interior angles.

From the given figure we conclude that:

[tex]\angle ZYM=\angle YZX+\angle ZXY[/tex]

Given:

[tex]\angle ZYM=115^o\\\\\angle YZX=(4k+5)^o\\\\\angle ZXY=(6k+10)^o[/tex]

Now put all the given values in the above expression, we get:

[tex]115^o=(4k+5)^o+(6k+10)^o[/tex]

[tex]115=4k+5+6k+10[/tex]

[tex]115=10k+15[/tex]

[tex]10k=115-15[/tex]

[tex]10k=100[/tex]

[tex]k=10[/tex]

Therefore, the value of 'k' is, [tex]10^o[/tex]