MHB Help with This: Get Assistance Now

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Vertical angles are pairs of angles that are opposite each other when two lines intersect, and they are always equal in measure. A linear pair of angles consists of two adjacent angles that form a straight line, making them supplementary, meaning their measures add up to 180 degrees. The degree measure of a straight line is 180 degrees. Given that angle 2 and the angle measuring 41 degrees are supplementary, angle 2 measures 139 degrees. Consequently, angle 3, being vertical to angle 2, also measures 139 degrees.
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look up the definitions for (1) a pair of vertical angles and (2) a linear pair of angles
 
Much the same but angle 2 and the angle with measure 41 degrees are "supplementary angles", together they make a straight line. What is the degree measure of a straight line? And while "vertical angles" is the easiest way to get the measure of angle 3, note that it and angle 2 also form a straight line. What does that tell you about getting the measure of angle 3 from the now known measure of angle 2?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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