Question

practice with measures involving angles and arcs formed by intersecting chords, secants, and tangents. what are the measures of angles 1 and 2? m∠1 = m∠2 = 53° 47°

Explanation:

Step1: Recall angle - chord - 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: Find measure of ∠1

The arcs intercepted by ∠1 are the arcs with measures 53° and 47°. So, $m\angle1=\frac{1}{2}(53 + 47)$.
$m\angle1=\frac{1}{2}(100)=50^{\circ}$

Step3: Find measure of ∠2

∠1 and ∠2 are vertical angles. Vertical angles are congruent. So, $m\angle2 = m\angle1$.
$m\angle2=50^{\circ}$

Answer:

$m\angle1 = 50^{\circ}$
$m\angle2 = 50^{\circ}$