(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°
Of course you already know everything parallel sides are equals
therefore the value of each variables will be as following :
left side = right side
3y-6=24
3y=24+6
3y=30
y=30/3
y=10
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5x+2=12
5x=12-2
5x=10
x=10/5
x=2
Ok well since it says the product of a number and 6 is 44 more than twice the number. and from this they got 6x=44+2x because it SAYS THE PRODUCT OF A NUMBER U DON'T KKNOW WHAT THE NUMBER IS SO U USE A VARIABLE WHICH IS 6X THEY GOT = 44 FROM THE PRODUCT AND 2X FROM MORE THAN TWICE THE NUMBER AND TWICE IS 2 AND U DON'T KNOW WHAT THE NUMBER IS SO ONCE AGAIN USE A VARIABLE
HOPE THIS HELPED
Value of x would equal 62
4 Pizzas. $14x4=$56 and you have $4 left over
