Question 1113624: Can someone help me find the measure of the angles of this circle: https://imgur.com/TeYcWwu
I only need the measures angle C, angle B, angle BSD, angle CSE, angle E, the measure of Arc BC
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's a reference you should find useful.
http://mathbitsnotebook.com/
the particular section you would be interested in is:
http://mathbitsnotebook.com/Geometry/Circles/CRAngles.html
here's my completed picture of your diagram.
you can see from the diagram that angle C and angle B are both equal to 26 degrees.
this is because both are inscribed angles to arc ED which is equal to 52 degrees.
those angles are therefore 1/2 * 52 = 26 degrees.
you can also see from the diagram that angles E and angle D are each 57 degrees.
this is because both are inscribed angles to arc CB which is equal to 114 degrees.
1/2 * 114 = 57 degrees.
how did we get arc BC = 114 degrees?
angle D is 57 degrees and is an inscribed angle of arc BC.
this makes angle D equal to 1/2 the measure of arc BC.
you get 57 = 1/2 * BC.
solve for BC to get BC = 114 degrees.
angle BSD is equal to 97 degrees.
angle CSE is also equal to 97 degrees because it is a vertical angle to angle BSD.
why is angle BSD equal to 97 degrees/
because it is part of triangle BSD and the sum of the angle of a triangle is always equal to 180 degrees.
angles B and D total 83 degrees.
97 + 83 = 180 degrees.
angle BSD has to be equal to 97 degrees.
i think that answers all your questions.
you said:
I only need the measures angle C, angle B, angle BSD, angle CSE, angle E, the measure of Arc BC
angle C is equal to 26 degrees, angle B is equal to 26 degrees, angle BSD is equal to 97 degrees, angle CSE is equal to 97 degrees, angle E is equal to 57 degrees, the measure of arc BC is equal to 114 degrees.
Answer by ikleyn(52821)  (Show Source):
You can put this solution on YOUR website! .
In this site, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
There is group of lessons on circles, their chords, secant and tangent lines
- A circle, its chords, tangent and secant lines - the major definitions
- The longer is the chord the larger its central angle is
- The chords of a circle and the radii perpendicular to the chords
- A tangent line to a circle is perpendicular to the radius drawn to the tangent point
- An inscribed angle in a circle (*)
- Two parallel secants to a circle cut off congruent arcs
- The angle between two chords intersecting inside a circle
- The angle between two secants intersecting outside a circle
- The angle between a chord and a tangent line to a circle
- Tangent segments to a circle from a point outside the circle
- The converse theorem on inscribed angles
- The parts of chords that intersect inside a circle
- Metric relations for secants intersecting outside a circle
- Metric relations for a tangent and a secant lines released from a point outside a circle
- Quadrilateral inscribed in a circle
- Quadrilateral circumscribed about a circle
My lessons in this site on solved problems for circles, their chords, secant and tangent lines are
- HOW TO bisect an arc in a circle using a compass and a ruler,
- HOW TO find the center of a circle given by two chords
- Solved problems on a radius and a tangent line to a circle
- Solved problems on inscribed angles
- A property of the angles of a quadrilateral inscribed in a circle
- An isosceles trapezoid can be inscribed in a circle
- HOW TO construct a tangent line to a circle at a given point on the circle
- HOW TO construct a tangent line to a circle through a given point outside the circle
- HOW TO construct a common exterior tangent line to two circles
- HOW TO construct a common interior tangent line to two circles
- Solved problems on chords that intersect within a circle
- Solved problems on secants that intersect outside a circle
- Solved problems on a tangent and a secant lines released from a point outside a circle
- Solved problems on tangent lines released from a point outside a circle
In this list, I marked by (*) the lesson most close to your problem.
The referred lessons are the part of this online textbook under the topic "Properties of circles, inscribed angles, chords, secants and tangents ".
Save the link to this online textbook together with its description
Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson
to your archive and use it when it is needed.
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