(9)
<em>x</em> ° = 1/2 (130° - 30°) = 50°
(due to a theorem about intersecting secants/tangents)
(11) The labeled angle subtends a minor arc of meaure 120°, which means the larger arc has a measure of 360° - 120° = 240°. Then
<em>x</em> ° = 1/2 (240° - 120°) = 60°
(due to the same theorem)
(13) The labeling here is a bit confusing. I'm not sure what the 70° is referring to. It occurs to me that it might be info from a different exercise, so that <em>y </em>° is the measure of the angle made by the tangent to the circle with a vertex of the pentagon, and <em>x</em> ° is the measure of each arc that passes over an edge of the pentagon.
Each arc makes up 1/5 of the circle's circumferece, so
<em>x</em> ° = 360°/5 = 72°
The pentagon is regular, so each of its interior angles have the same measure of 108°. (Why 108°? Each exterior angle measures 360°/5 = 72°, since the exterior angles sum to 360°. Interior and exterior angles are supplementary, so the interior angles measure 180° - 72° = 108° each.)
The angles formed by the tangent to the circle are supplementary, so that
<em>y</em> ° + 108° + <em>y</em> ° = 180°
2<em>y</em> ° = 72°
<em>y</em> ° = 36°
The answer is B. 5.6 kilometers. 5.592 miles are in 9 kilometers which would round up to 5.6
If you graduated in 2010 then you started high school in....
2010-4 years (university education years) - (3 high school years)= 2003
you started high school education in 2003
0.123 = 41/333 hope this helps :)
