Question

In the triangle, suppose that m < K = (x+7)°, m< L = (4x+5)°, and m< M = (3x)°.

Answer 1

As the sum of the interior angles of a triangle equals 180°, we can build the following relation:

$m\angle K+m\angle L+m\angle M=180$

Replacing the expressions given:

$(x+7)+(4x+5)+(3x)=180$

Simplifying the equation we get:

$\begin{gathered} x+7+4x+5+3x=180 \\ 8x+12=180 \\ x=\frac{180-12}{8} \\ x=21 \end{gathered}$

Then, to get the value of each angle we have to substitute this value in each expression given.

• m∠K

$m\angle K=x+7=21+7=28$

• m∠L

$m\angle L=4x+5=4\cdot21+5=84+5=89$

• m∠M

$m\angle M=3x=3\cdot21=63$

Answer:

• Equation

$(x+7)+(4x+5)+(3x)=180$

• m∠K = 28°

,

• m∠L = 89°

,

• m∠M = 63°