Question

1. in $\triangle mnp$, if $m\angle m = (4x - 3)°$, $m\angle n = (9x - 6)°$, and $m\angle p = (6x - 1)°$, find the value of $x$ and the measure of each angle.

$x = \underline{\quad\quad}$
$m\angle m = \underline{\quad\quad}$
$m\angle n = \underline{\quad\quad}$
$m\angle p = \underline{\quad\quad}$

1. in $\triangle bst$...

Explanation:

Step1: Recall triangle angle sum theorem

The sum of the interior angles of a triangle is \(180^\circ\). So, \(m\angle M + m\angle N + m\angle P = 180^\circ\).
Substitute the given angle expressions: \((4x - 3)+(9x - 6)+(6x - 1)=180\).

Step2: Combine like terms

Combine the \(x\) terms and the constant terms: \(4x+9x + 6x-3-6 - 1=180\).
\(19x-10 = 180\).

Step3: Solve for x

Add 10 to both sides: \(19x=180 + 10=190\).
Divide both sides by 19: \(x=\frac{190}{19}=10\).

Step4: Find each angle

• \(m\angle M=(4x - 3)^\circ\). Substitute \(x = 10\): \(4(10)-3=40 - 3 = 37^\circ\).
• \(m\angle N=(9x - 6)^\circ\). Substitute \(x = 10\): \(9(10)-6=90 - 6 = 84^\circ\).
• \(m\angle P=(6x - 1)^\circ\). Substitute \(x = 10\): \(6(10)-1=60 - 1 = 59^\circ\).

Answer:

\(x = 10\)
\(m\angle M = 37^\circ\)
\(m\angle N = 84^\circ\)
\(m\angle P = 59^\circ\)