Question
Two lines inside a circle, lines upper A upper C and upper B upper D, intersect at point E.
Chord AC¯¯¯¯¯¯¯¯
intersects chord DB¯¯¯¯¯¯¯¯
at point E
. If the mAD=67°
and mBC=87°
, then find the m∠AED
.
Chord AC¯¯¯¯¯¯¯¯
intersects chord DB¯¯¯¯¯¯¯¯
at point E
. If the mAD=67°
and mBC=87°
, then find the m∠AED
.
Answers
GPT-4o mini
To find the measure of angle \( \angle AED \), we can use the fact that when two chords intersect inside a circle, the measures of the angles formed by the intersection are related to the arcs intercepted by these angles.
Given:
- \( m\angle ADB = 67^\circ \)
- \( m\angle BCA = 87^\circ \)
Using the property of angles formed by intersecting chords, we have:
\[
m\angle AED = \frac{1}{2} (m\angle ADB + m\angle BCA)
\]
Substituting the known values:
\[
m\angle AED = \frac{1}{2} (67^\circ + 87^\circ)
\]
\[
m\angle AED = \frac{1}{2} (154^\circ)
\]
\[
m\angle AED = 77^\circ
\]
Thus, the measure of \( \angle AED \) is \( \boxed{77^\circ} \).
Given:
- \( m\angle ADB = 67^\circ \)
- \( m\angle BCA = 87^\circ \)
Using the property of angles formed by intersecting chords, we have:
\[
m\angle AED = \frac{1}{2} (m\angle ADB + m\angle BCA)
\]
Substituting the known values:
\[
m\angle AED = \frac{1}{2} (67^\circ + 87^\circ)
\]
\[
m\angle AED = \frac{1}{2} (154^\circ)
\]
\[
m\angle AED = 77^\circ
\]
Thus, the measure of \( \angle AED \) is \( \boxed{77^\circ} \).