Question

Consider the triangle below

Answer 1

`m\angle M=90`

`m\angle A=63`

`m\angle N=27`

`\Delta MAN` is a right triangle.

Explanation:

Since we know that sum of all angles of triangles equals to 180 degrees.

To find the measure of our given angles we will have to find the value of x. The value of x can be found by equating the measure of all angles of our given triangle with 180.

`4x-5+9x-9+10x+10=180`

`23x-14+10=180`

`23x-4=180`

`23x=180+4`

`23x=184`

`x=(184)/(23)`

`x=8`

Now let us find measure of each angle by substituting value of x in given expressions.

`m\angle M=10*x+10`

`m\angle M=10*8+10`

`m\angle M=80+10`

`m\angle M=90`

Therefore, measure of angle M is 90 degrees.

`m\angle A=9*x-9`

`m\angle A=9*8-9`

`m\angle A=72-9`

`m\angle A=63`

Therefore, measure of angle A is 63 degrees.

`m\angle N=4*x-5`

`m\angle N=4*8-5`

`m\angle N=32-5`

`m\angle N=27`

Therefore, measure of angle N is 27 degrees.

From the measures of angles we can say that triangle MAN is a right triangle.