Question

question 2
if ( mangle a+mangle b=mangle c,mangle a = 29^{circ}), and ( mangle b = 71^{circ}), then what type of angle
is (angle c)?
hint: plug in the values for (angle a) and (angle b). then use your vocabulary sheet to find
what type of angle (angle c) is.
a acute
b obtuse
c right

Explanation:

Step1: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle A + m\angle B+m\angle C=180^{\circ}\).
Given \(m\angle A = 29^{\circ}\) and \(m\angle B = 71^{\circ}\). Substitute these values into the equation: \(29^{\circ}+71^{\circ}+m\angle C = 180^{\circ}\).

Step2: Solve for \(m\angle C\)

First, simplify the left - hand side of the equation: \(29 + 71+m\angle C=180\). Since \(29 + 71=100\), the equation becomes \(100^{\circ}+m\angle C=180^{\circ}\).
Then, subtract \(100^{\circ}\) from both sides: \(m\angle C=180^{\circ}-100^{\circ}\). So, \(m\angle C = 80^{\circ}\).

Step3: Classify the angle \(\angle C\)

An acute angle is an angle whose measure is between \(0^{\circ}\) and \(90^{\circ}\). Since \(0^{\circ}<80^{\circ}<90^{\circ}\), \(\angle C\) is an acute angle.

Answer:

A. acute