Question

5 m 3x° (3x + 2)° n (14x - 2)° p m∠m =
m∠n =
m∠p =

Explanation:

Step1: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(3x+(3x + 2)+(14x-2)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((3x+3x + 14x)+(2 - 2)=180\), which gives \(20x=180\).

Step3: Solve for \(x\)

Divide both sides of the equation by 20: \(x=\frac{180}{20}=9\).

Step4: Find the measure of angle \(M\)

Substitute \(x = 9\) into the expression for \(\angle M\). \(m\angle M=3x\), so \(m\angle M=3\times9 = 27^{\circ}\).

Step5: Find the measure of angle \(N\)

Substitute \(x = 9\) into the expression for \(\angle N\). \(m\angle N=3x + 2\), so \(m\angle N=3\times9+2=27 + 2=29^{\circ}\).

Step6: Find the measure of angle \(P\)

Substitute \(x = 9\) into the expression for \(\angle P\). \(m\angle P=14x-2\), so \(m\angle P=14\times9-2=126-2 = 124^{\circ}\).

Answer:

\(m\angle M = 27^{\circ}\)
\(m\angle N = 29^{\circ}\)
\(m\angle P = 124^{\circ}\)