In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer.

< CFE = 40°

Step-by-step explanation:

To better understand the solution, see attachment for the diagram.

Given:

BC parallel to DE

Measure of Arc BD = 58°

Measure of Arc DE = 142°

First step: Draw a diameter that passes through the centre of the circle and name it. In this case, the diameter is line ST.

The line ST divides the arc BD and arc DE into half.

That is:

Arc SC = 1/2(arc BC) =1/2(58)

Arc SC = 29°

Arc TE = 1/2(arc DE) =1/2(142)

Arc TE = 71°

Arc SC + Arc CE + Arc TE = 180° (Sum of angles in a semicircle

29° + Arc CE  + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Inscribed angle = 1/2(intercepted angle)

<CFE = 1/2(Arc CE )

<CFE = 1/2(80)

< CFE = 40°

$450 is the answer.

step-by-step explanation:

30% of 450 = 135

450-135=315

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt