Question

What is the value of k?

Please answer ASAP, Thank you :)

Answer 1

k=10

Explanation:

∠ZYX= 180-115= 65 these are supplementary angles adding up to 180°.

The interior angles in the triangle should add up to 180°

Adding the values and then equating to 180° we get the following equation.

65+(4k+5)+(6k+10)=180°

simplifying we get: 80+10k=180

10k=180-80

10k=100

k=10

Answer 2

k = 10

Explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ZYM is an exterior angle of the triangle and

∠'s YZX and ZXY are the 2 opposite interior angles, hence

4k + 5 + 6k + 10 = 115

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10