Question

given: a circle with inscribed quadrilateral abcd prove: ∠a and ∠c are supplementary. 1. let m∠dcb = a°. then m∠dab = 360 - a. 2. by the inscribed - angle theorem, m∠a = a/2. 3. also by the inscribed - angle theorem, m∠c = (360 - a)/2. 4. therefore, m∠a + m∠c = a/2+(360 - a)/2, which simplifies to:

Explanation:

Step1: Combine the fractions

We have \(m\angle A + m\angle C=\frac{a}{2}+\frac{360 - a}{2}\). Since the denominators are the same, we can add the numerators: \(\frac{a+(360 - a)}{2}\).

Step2: Simplify the numerator

Simplify \(a+(360 - a)\): \(a + 360 - a=360\). So the fraction becomes \(\frac{360}{2}\).

Step3: Calculate the result

\(\frac{360}{2}=180\).

Answer:

180