Question

In the triangle below, ZN is a right angle. Suppose that mZL= (5x+15) and mZM=(4x+3) º.(a) Write an equation to find x. Make sure you use an "=" sign in your answer.Equation: 0DEOM*<(4x + 3)Х5?(b) Find the degree measure of each angle.*( (5*+ 15)m LL =?1=mZN =m LM=

Answer 1

As per given by the question,

There are given tha a right angle triangle and ,

The given angle is;

`m\angle L=(5x+15)^(\circ),\text{ m}\angle m=(4x+3)^(\circ)`

Now,

The sum of the angles in triangle is 180 degree. A right triangle has one angle of 90 degree.

So,

The sum of the other two angle will be 90 degree.

Then,

From triangle MNL;

`(5x+15)+(4x+3)=90^(\circ)`

Fro above equation, find the value of x;

`\begin{gathered} (5x+15)+(4x+3)=90^(\circ) \\ 5x+15+4x+3=90 \\ 9x+18=90 \\ 9x=90-18 \\ 9x=72 \end{gathered}`

Then,

`\begin{gathered} 9x=72, \\ x=(72)/(9) \\ x=8 \end{gathered}`

So, the value of x is 8.

Now,

For the angle L,

Put the value of x in equation of angle L,

`\begin{gathered} m\angle L=(5x+15)^(\circ) \\ m\angle L=5(8)+15 \\ m\angle L=40+15 \\ m\angle L=55^(\circ) \end{gathered}`

For the angle M,

`\begin{gathered} m\angle M=(4x+3)^(\circ) \\ m\angle M=4(8)+3 \\ m\angle M=32+3 \\ m\angle M=35 \end{gathered}`

Now,

For the angle N;

The angle N is,

`m\angle N=90^(\circ)`

Hence, the value of x is 8, and the angle L is 55 degree, angle M is 35 degree, and the angle N is 90 degree,