Question

step angle reason
1 ( m angle a d b = 98 ^ { circ } ) given
2 ( m angle b = 45 ^ { circ } ) given
try ( m angle ) ( b a d ) ( = ) ( 37 ) ( ^ { 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
perpendicular lines form right angles

Explanation:

Step1: Recall the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In \(\triangle ABD\), we know two angles (\(\angle ADB = 98^{\circ}\) and \(\angle B=45^{\circ}\)), and we want to find \(\angle BAD\).
Let \(\angle BAD=x\). According to the formula \(x+\angle B+\angle ADB = 180^{\circ}\).

Step2: Substitute the given values into the formula

Substitute \(\angle ADB = 98^{\circ}\) and \(\angle B = 45^{\circ}\) into \(x+\angle B+\angle ADB=180^{\circ}\).
We get \(x + 45^{\circ}+98^{\circ}=180^{\circ}\).
First, add \(45^{\circ}\) and \(98^{\circ}\): \(45 + 98=143\), so the equation becomes \(x+143^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(143^{\circ}\) from both sides of the equation \(x+143^{\circ}=180^{\circ}\).
\(x=180^{\circ}-143^{\circ}\).
\(x = 37^{\circ}\).

Answer:

The reason is "Sum of angles in a triangle".