Question

In 'MNP, if m∠M = (4x - 3)°, m∠N = (9x - 6)°, and m∠P = (6x - 1)°, find the value of x and the measure of each angle.

a) x = 5, m∠M = 17°, m∠N = 39°, m∠P = 29°
b) x = 2, m∠M = 5°, m∠N = 9°, m∠P = 11°
c) x = 4, m∠M = 13°, m∠N = 30°, m∠P = 23°
d) x = 6, m∠M = 21°, m∠N = 45°, m∠P = 35°

Answer 1

To find the value of x and the measure of each angle in triangle MNP, set up and solve equations using the given information. The value of x is 10, and the measure of each angle is m∠M = 37°, m∠N = 84°, and m∠P = 59°.

Step-by-step explanation:

To find the value of x and the measure of each angle in the triangle MNP, we can set up equations using the given information:

1. 
   
3. m∠M = (4x - 3)°
4. 
   
6. m∠N = (9x - 6)°
7. 
   
9. m∠P = (6x - 1)°
10. 
    
12. The sum of the angles in a triangle is 180°

To solve for x, we can set up an equation:

(4x - 3) + (9x - 6) + (6x - 1) = 180

Simplifying the equation, we get:

19x - 10 = 180

19x = 190

x = 10

To find the measure of each angle, we substitute x = 10 into the given equations:

m∠M = (4x - 3) = (4(10) - 3) = 37°

m∠N = (9x - 6) = (9(10) - 6) = 84°

m∠P = (6x - 1) = (6(10) - 1) = 59°