Question

12. For triangle MNP shown, find the value of x

and the measure of each of the three angles
M
/(2x – 1)º (2x + 1))​

Answer 1

`x=36\°\\\angle P=71 \°,\angle N=73 \°,\angle M=36 \°`

Explanation:

Given:

The triangle is shown below.

We know that the sum of all interior angles of a triangle is equal to 180°.

Therefore,

`\angle M+\angle N+\angle P=180 \°\\\\x+2x+1+2x-1=180\°\\\\5x=180\°\\\\x=(180)/(5)\\\\x=36\°`

Now, plugging the value of 'x' in each angle measure and determining its values. We get:

`\angle M=x=36\°\\\angle P=2x-1=2(36)-1=72-1=71\°\\\angle N=2x+1=2(36)+1=72+1=73\°`

Therefore, the value of 'x' is 36° and the measure of the three angles are 36°, 71° and 73°.