Question

section 5 - topic 2 introduction to triangles - part 2

1. consider the figure below.

determine the measure of each interior angle of △man and classify the triangle.
m∠a =
m∠m =
m∠n =
△man is a(n) ______________ triangle.

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $(x)+(x - 48)+(2x-164)=180$.

Step2: Combine like - terms

$x+x + 2x-48-164 = 180$.
$4x-212 = 180$.

Step3: Solve for x

Add 212 to both sides: $4x=180 + 212$.
$4x=392$.
Divide both sides by 4: $x=\frac{392}{4}=98$.

Step4: Find the measure of each angle

For $\angle A$:
$m\angle A=x$. Substitute $x = 98$, so $m\angle A=98^{\circ}$.
For $\angle M$:
$m\angle M=x - 48$. Substitute $x = 98$, so $m\angle M=98 - 48=50^{\circ}$.
For $\angle N$:
$m\angle N=2x-164$. Substitute $x = 98$, so $m\angle N=2\times98-164=196 - 164 = 32^{\circ}$.

Step5: Classify the triangle

Since $m\angle A=98^{\circ}>90^{\circ}$, $\triangle MAN$ is an obtuse - angled triangle.

Answer:

$m\angle A = 98^{\circ}$
$m\angle M = 50^{\circ}$
$m\angle N = 32^{\circ}$
$\triangle MAN$ is an obtuse - angled triangle.