Question

2 if ( moverparen{ab}=30^{circ} ) and ( moverparen{cd}=110^{circ} ), find ( mangle e ).

a. ( 70^{circ} ) b. ( 15^{circ} ) c. ( 30^{circ} ) d. ( 40^{circ} )
3 find the value of each variable.

a. ( x = 75^{circ} ) and ( y = 78^{circ} )
b. ( x = 78^{circ} ) and ( y = 65^{circ} )
c. ( x = 102^{circ} ) and ( y = 115^{circ} )
d. ( x = 71.5^{circ} ) and ( y = 71.5^{circ} )

Explanation:

Step1: Recall the formula for the measure of an angle formed by two secants

The measure of an angle formed by two secants intersecting outside a circle is given by \(m\angle E=\frac{1}{2}(m\overarc{CD}-m\overarc{AB})\)

Step2: Substitute the given values

We are given that \(m\overarc{AB} = 30^{\circ}\) and \(m\overarc{CD}=110^{\circ}\). Substitute these values into the formula:

$$
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Answer:

D. \(40^{\circ}\)