Question

drag the correct answers into the boxes. show hints m∠atb = 1/2 = 1/2 = 1/2 = (36° + 68°) 52° (mab - mdc) (mab + mdc) (36° - 68°) 104° 32° 16°

Explanation:

Step1: Recall angle - arc relationship

The measure of an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The arcs intercepted by $\angle ATB$ are $\overset{\frown}{AB}$ and $\overset{\frown}{DC}$ with measures $36^{\circ}$ and $68^{\circ}$ respectively.

Step3: Apply the formula

$m\angle ATB=\frac{1}{2}(m\overset{\frown}{AB} + m\overset{\frown}{DC})=\frac{1}{2}(36^{\circ}+68^{\circ})$.

Step4: Calculate the sum inside the parentheses

$36^{\circ}+68^{\circ}=104^{\circ}$.

Step5: Calculate the angle measure

$\frac{1}{2}\times104^{\circ} = 52^{\circ}$.

Answer:

$m\angle ATB=\frac{1}{2}(m\overset{\frown}{AB}+m\overset{\frown}{DC})=\frac{1}{2}(36^{\circ}+68^{\circ})=\frac{1}{2}(104^{\circ}) = 52^{\circ}$
So the blanks should be filled as follows:
First blank: $(m\overset{\frown}{AB}+m\overset{\frown}{DC})$
Second blank: $(36^{\circ}+68^{\circ})$
Third blank: $104^{\circ}$
Fourth blank: $52^{\circ}$