✅ 10th Grade Geometry: Angles of Intersecting Chords Quiz
✅ 10th Grade Geometry: Angles of Intersecting Chords Quiz
Two chords intersect inside a circle. The intercepted arcs measure $50^\circ$ and $70^\circ$. What is the measure of the angle formed by the intersecting chords?
A) $60^\circ$B) $50^\circ$
C) $70^\circ$
D) $120^\circ$
Chords AB and CD intersect at point E inside a circle. If arc AC measures $40^\circ$ and arc BD measures $100^\circ$, what is the measure of angle AEC?
A) $60^\circ$B) $70^\circ$
C) $80^\circ$
D) $140^\circ$
An angle formed by two intersecting chords measures $75^\circ$. If one of the intercepted arcs measures $90^\circ$, what is the measure of the other intercepted arc?
A) $60^\circ$B) $45^\circ$
C) $75^\circ$
D) $150^\circ$
Two chords intersect inside a circle, forming an angle of $60^\circ$. If one of the intercepted arcs measures $50^\circ$, what is the measure of the arc intercepted by the vertical angle?
A) $70^\circ$B) $60^\circ$
C) $120^\circ$
D) $100^\circ$
Chords PQ and RS intersect at point T inside a circle. If arc PR measures $80^\circ$ and arc QS measures $120^\circ$, what is the measure of angle PTS?
A) $100^\circ$B) $80^\circ$
C) $120^\circ$
D) $140^\circ$
Two chords intersect inside a circle. The intercepted arcs are represented by $2x^\circ$ and $3x^\circ$. If the angle formed by the chords is $100^\circ$, what is the value of $x$?
A) $20$B) $40$
C) $50$
D) $10$
Chords AB and CD intersect at point E inside a circle. Angle AEC measures $80^\circ$. Arc AC is represented by $ (x+20)^\circ $ and arc BD is represented by $ (2x-10)^\circ $. Find the value of $x$.
A) $30$B) $40$
C) $50$
D) $60$
Two chords intersect inside a circle. One of the angles formed is $ (3x+10)^\circ $. The intercepted arcs for this angle measure $60^\circ$ and $80^\circ$. What is the value of $x$?
A) $10$B) $20$
C) $30$
D) $40$
If two chords intersect inside a circle and intercept arcs of $50^\circ$ and $70^\circ$, what is the measure of the obtuse angle formed at the intersection?
A) $60^\circ$B) $110^\circ$
C) $120^\circ$
D) $130^\circ$
Two chords intersect inside a circle. One of the angles formed measures $95^\circ$. If one of the intercepted arcs measures $110^\circ$, what is the measure of the arc intercepted by the vertical angle?
A) $80^\circ$B) $95^\circ$
C) $70^\circ$
D) $190^\circ$
If the sum of the measures of two intercepted arcs by an angle formed by intersecting chords is $180^\circ$, what is the measure of the angle?
A) $45^\circ$B) $60^\circ$
C) $90^\circ$
D) $180^\circ$
Two chords intersect inside a circle. One of the angles formed measures $x^\circ$. The two intercepted arcs for this angle measure $ (0.5x+30)^\circ $ and $ (0.5x+50)^\circ $. Find the value of $x$.
A) $60$B) $70$
C) $80$
D) $90$
In a circle, two chords intersect. One angle formed measures $ (2y+10)^\circ $. The intercepted arcs for this angle are in the ratio 2:3. The sum of these two arcs is $ (6y-20)^\circ $. Find the measure of the angle.
A) $40^\circ$B) $50^\circ$
C) $60^\circ$
D) $70^\circ$
Two chords intersect inside a circle. One of the angles formed measures $80^\circ$. One of the intercepted arcs for this angle is $60^\circ$. The other two arcs intercepted by the vertical angles are in the ratio 3:5. Find the measure of the largest arc in the entire circle.
A) $100^\circ$B) $120^\circ$
C) $125^\circ$
D) $150^\circ$
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