Question 1159927
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The four arcs together make the whole 360 degrees of the circle.<br>
{{{x+4x+4x+3x = 360}}}
{{{12x = 360}}}
{{{x = 30}}}<br>
(a) The measures of the arcs are 30, 120, 120, and 90 degrees.<br>
(b) The measure of angle P is half the difference between the measures of the two intercepted arcs: (1/2)(120-30) = 45 degrees.<br>
(c) Angle PUT intercepts arc RST, which has measure 30+120 = 150 degrees.  The measure of the angle is half the measure of the intercepted arc: 150/2 = 75 degrees.<br>