Question

question 16 (5 points)
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if ( mangle adc = 164^{circ} ) and ( overline{db} ) is the angle bisector of ( angle adc ), find ( mangle bdc ).
a) ( 100^{circ} )
b) ( 82^{circ} )
c) ( 328^{circ} )
d) ( 164^{circ} )

Explanation:

Step1: Recall the definition of angle bisector

An angle bisector divides an angle into two equal parts.

Step2: Calculate \(m\angle BDC\)

Since \(DB\) is the angle bisector of \(\angle ADC\) and \(m\angle ADC = 164^{\circ}\), then \(m\angle BDC=\frac{1}{2}m\angle ADC\).
Substitute \(m\angle ADC = 164^{\circ}\) into the formula: \(m\angle BDC=\frac{1}{2}\times164^{\circ}=82^{\circ}\)

Answer:

B. \(82^{\circ}\)