Question

step angle reason
1 $m\angle adb = 98^{circ}$ given
2 $m\angle b = 45^{circ}$ given
3 $m\angle bad = 37^{circ}$ sum of angles in a triangle
4 $m\angle adc = 82^{circ}$ linear pair (or triple)
try $m\angle c = 61^{circ}$ select a reason
vertical angles
linear pair (or triple)
congruent angles
sum of angles in a triangle
sum of angles in a quadrilateral
base angle of an isosceles triangle
angle bisector definition
corresponding angles
alternate interior angles
alternate exterior angles
same - side interior angles
angle addition postulate
angle subtraction postulate

Explanation:

Step1: Analyze the formula for the sum of angles in a triangle

In triangle \(ADC\), the sum of the interior angles of a triangle is \(180^{\circ}\). The formula is \(m\angle CAD + m\angle ADC+ m\angle C=180^{\circ}\).

Step2: Substitute the known values

We know from step 3 that \(m\angle BAD = 37^{\circ}\) (assuming \(\angle CAD=\angle BAD\) if there is no other - angle splitting information shown in the figure in a wrong - way), and from step 4 \(m\angle ADC = 82^{\circ}\). Substituting into the formula \(m\angle C=180-(m\angle CAD + m\angle ADC)\).

$$m\angle C=180-(37 + 82)$$

$$m\angle C=180 - 119$$

$$m\angle C = 61^{\circ}$$

Answer:

Sum of angles in a triangle