Question

13. In triangle MNP, if
measure M = 4x - 3, measure N = 9x - 6, and measure P = 6x - 1, find x and the measure of each angle.​

Answer 1

Answer:

Part a) $x=10$

Part b) m∠M=37°, m∠N=84°, m∠P=59°

Step-by-step explanation:

Part a) Find out the measure of each angle

we know that

The sum of the internal angles in a triangle must be equal to 180 degrees

In this problem

m∠M+m∠N+m∠P=180°

substitute the given values

$(4x-3)\°+(9x-6)\°+(6x-1)\°=180\°$

Solve for x

Combine like terms

$19x-10=180$

Adds 10 both sides

$19x=180+10$

$19x=190$

Divide by 19 both sides

$x=10$

Part b) Find the measure of each angle

1) m∠M=(4x-3)°

substitute the value of x

m∠M=(4(10)-3)=37°

2) m∠N=(9x-6)°

substitute the value of x

m∠N=(9(10)-6)=84°

3) m∠P=(6x-1)°

substitute the value of x

m∠P=(6(10)-1)=59°

Answer 2

Angles in a triangle add up to 180 degrees.

The value of x is 10, and the measures of the angles are 37. 59 and 84 degrees

The given parameters are:

$\mathbf{M = 4x - 3}$

$\mathbf{N = 9x - 6}$

$\mathbf{P = 6x - 1}$

So, we have:

$\mathbf{M + N + P = 180}$

Substitute known values

$\mathbf{4x - 3 + 9x - 6 + 6x -1 = 180}$

Collect like terms

$\mathbf{4x + 9x + 6x = 180 + 1 + 6 + 3}$

$\mathbf{19x = 190}$

Divide both sides by 19

$\mathbf{x = 10}$

So, we have:

$\mathbf{M = 4(10) - 3 = 37}$

$\mathbf{N = 9(10) - 6 = 84}$

$\mathbf{P = 6(10) - 1 = 59}$

Hence, the value of x is 10, and the measures of the angles are 37. 59 and 84 degrees

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