Two secants meet outside the circle, forming an angle of 42 degrees. if the larger intercepted arc is 120 degrees, find the smaller intercepted arc

36°

Step-by-step explanation:

An angle whose vertex lies outside a circle whose sides are 2 secants of the circle is

angle = ( larger arc - smaller arc ), that is

42 = ( 120 - smaller ) ← multiply both sides by 2

84 = 120 - smaller, hence

smaller = 120 - 84 = 36°

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

your answer is a

step-by-step explanation:

4*4*4*4=256