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By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle POR of the intercepted arc PR is 90°. Therefore, MPR=12mPOR =12(90°) =45°.
In geometry, an inscribed angle is the angle formed in the interior of a circle when two secant lines (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.
Given the measure of an arc in degrees, the length of the arc can be found by multiplying the quotient of the given angle and 360 degrees to the length of the circumference of the circle.
The measure of an inscribed angle is half the measure of the intercepted arc. That is, Mac=12mAOC. This leads to the corollary that in a circle any two inscribed angles with the same intercepted arcs are congruent.
An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle. ... It says that the measure of the intercepted arc is twice that of the inscribed angle.
The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle 2 that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle.
To find arc length, start by dividing the arc's central angle in degrees by 360. Then, multiply that number by the radius of the circle. Finally, multiply that number by 2 × pi to find the arc length.
Using a Protractor The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree.
To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2.
To measure an acute angle without a protractor, start by drawing a vertical line connecting the 2 rays of the angle to form a right triangle. Note that the angle formed by the adjacent side of the triangle and the opposite side measures 90 degrees. Next, measure the length of the adjacent side to find the run.
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