253,510 views
25 votes
25 votes
In the triangle, suppose that m < K = (x+7)°, m< L = (4x+5)°, and m< M = (3x)°.

In the triangle, suppose that m < K = (x+7)°, m< L = (4x+5)°, and m< M = (3x-example-1
User Zygimantas Gatelis
by
2.8k points

1 Answer

17 votes
17 votes

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=(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°

User Gerardnimo
by
2.9k points