Question

Enzo drew Triangle K L N. In Enzo's triangle, Measure of angle K is represented as x degrees. The measure of Angle L is 5 times Measure of angle K. The measure of Angle N is 16 degrees less than 8 times Measure of angle K. Which statements must be true about the angle measures of Enzo's triangle? Check all that apply. Measure of angle K = x degrees Measure of angle L = (5 x) degrees Measure of angle N = (16 minus 8 x) degrees Measure of angle K + measure of angle L = measure of angle N Measure of angle K + measure of angle L + measure of angle N = 180 degrees

Answer 1

145

Explanation:

Answer 2

Answer: (1) Measure of angle K = x degrees

(12) Measure of angle L = (5x) degrees

(3) Measure of angle k + Measure of angle L + Measure of angle N = 180 degrees

Step-by-step explanation: First of all, what we have is a triangle, and one of the properties of a triangle is all three angles add up to 180 degrees. This simply means that the addition of angles K and L and N would be equal to 180 degrees.

The question states that angle K is represented as x degrees, and angle L is 5 times the measure of angle K. Therefore, if K is x degrees, then L is 5 times x, which becomes 5x degrees. Also, angle N is given as 16 degrees less than 8 times the measure of angle K (x degrees). Eight times the measure of angle K is given as 8x. Sixteen degrees less than 8x would now become, 8x - 16 (degrees). Therefore, the angles have been derived as;

Angle K = x degrees

Angle L = 5x degrees

Angle N = 8x - 16 degrees

Having known that one of the properties of any triangle is all angles adding up to 180 degrees, we can now derive the following equation;

x + 5x + 8x - 16 = 180

14 x - 16 = 180

Add 16 to both sides of the equation

14x = 196

Divide both sides of the equation by 14

x = 14

Therefore, angle K = 14 degrees (x), angle L = 70 degrees (5x) and angle N = 96 degrees (8x - 16)

*14 + 70 + 96 = 180*