Question

A projected image appears as an isosceles trapezoid.

How many degrees larger do the angles in the lower left and lower right corners each need to be in order to form a rectangular image?

A. 1°
B. 9°
C. 11°
D. 19°

Answer 1

7x + 4 + 9x = 180
16x = 176
x = 11

9x = 9x11 = 99
7x + 4 = 7(11) + 4 = 77 + 4 = 81

in order to form a rectangular image, each angle needs to be equal 90 degreesn

99 - 9 = 90
81 + 9 = 90

answer

B. 9°

Answer 2

B. 9°

Explanation:

The given figure is an isosceles trapezoid.

Isosceles trapezoid means the non parallel sides must be equal.

In a trapezoid adjacent angles add upto 180 degrees. We are going to use this property to solve this problem.

In order to make the isosceles trapezoid to the rectangle, the top angles must be 90 degrees.

Given: (7x + 4) and 9x are adjacent angles that are add upto 180 degrees.

So, 7x + 4 + 9x = 180

Simplify the above equation, we get

16x + 4 = 180

16x = 180 - 4

16x = 176

Dividing both sides by 16, we get

x = 176/18

x = 11

Now let's find the each angle measures by plugging in x = 11

7x + 4 = 7(11) + 4 = 77 + 4 = 81 degrees

9x = 9x11 = 99 degrees

We are asked how many degree larger do the angles in the lower left and lower right corner should adjusted

In the lower left, we need to 9 degrees

81 + 9 = 90

In the lower right, we have to subtract 9 degrees.

99 - 9 = 90

So the answer is B. 9°