Question

if m ad=20° and m BC =30°,then <1=

Answer 1

When two chords intersect inside a circle, the measure of the angle formed is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Then:

$m\angle1=\frac{1}{2}(mAD+mBC)$

Substitute mAD=20° and mBC=30°:

$\begin{gathered} \Rightarrow m\angle1=\frac{1}{2}(20+30) \\ =\frac{1}{2}(50) \\ =25 \end{gathered}$

Therefore, the answer is:

$25^{\circ}$