Question

question 31 (5 points)
listen
in the given figure, find ( mangle bdc ), given that ( mangle adb = 53^{circ} ) and ( mangle adc = 82^{circ} ).
( 29^{circ} )
( 98^{circ} )
( 37^{circ} )
( 135^{circ} )

Explanation:

Step1: Analyze the relationship between angles

We know that \(m\angle ADC=m\angle ADB + m\angle BDC\) (angle - addition postulate).

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

Rearrange the formula: \(m\angle BDC=m\angle ADC - m\angle ADB\).
Substitute the given values: \(m\angle BDC = 82^{\circ}-53^{\circ}\).
Calculate: \(m\angle BDC=29^{\circ}\).

Answer:

\(29^{\circ}\) (the first option)