Question

find ( mangle d ).( mangle d = square^circ )

Explanation:

Step1: Calculate arc ADC measure

First, find the measure of arc \(ADC\) by adding the given arcs:
\(m\overset{\frown}{ADC} = m\overset{\frown}{AB} + m\overset{\frown}{BC} = 98^\circ + 102^\circ = 200^\circ\)

Step2: Apply inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. For \(\angle D\), the intercepted arc is \(ABC\):
\(m\angle D = \frac{1}{2} \times m\overset{\frown}{ABC}\)
\(m\angle D = \frac{1}{2} \times 200^\circ\)

Answer:

\(100^\circ\)