Answer:
136°
Explanation:
Theorem: The measure of the angle formed by a tangent and a chord is equal to one-half the measure of the intercepted arc.
In the diagram below, PR is the chord, PRS is the tangent, and PQR is the intercepted arc.
Per the theorem,
mPRS = ½mPQR
mPQR = 2mPRS = 2 × 68° = 136°
The measure of the intersected arc is 136°.
Theorem: The measure of the angle formed by a tangent and a chord is equal to half the measure of the intercepted arc.
The diagram below shows the chord PR, the tangent PRS, and the intercepted arc PQR.
This is theorized,
12mPQR = mPRS
mPQR=2mPRS=2 68°=136°
The intersecting arc has a 136° length.
Thales of Miletus, who lived and worked around 600 BC, is credited with some of the earliest geometric arguments that are still in use today.
In specifically, he is credited with proving the following five theorems: Any angle scribed in a circle is divided by any diameter, any angle scribed in a semicircle is a straight angle (90°), and opposite Two triangles must be congruent (of the same shape and size), the "vertical"angles created by the intersection of two lines must be equal, and isosceles triangles must have equal base angles.
The English mathematician Thomas Heath (1861–1940) presented what is now known as Thales' rectangle (see the picture) as a demonstration of (5) that would have been consistent with what was known in Thales' era, despite the fact that none of Thales' original proofs have survived.
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