Answer:
1. B. x = 11
2. E. [tex]m\angle BEF=140^{\circ}[/tex]
3. D. 4.3 in
4. D. 40.8 ft
Step-by-step explanation:
1. By Angle Addition Postulate,
[tex]m\angle KLM=m\angle KLV+m\angle VLM[/tex]
Since
[tex]m\angle KLV=34^{\circ}\\ \\m\angle KLM=14x+19\\ \\m\angle VLM=12x+7,[/tex]
then
[tex]14x+19=34+12x+7\\ \\14x-12x=34+7-19\\ \\2x=22\\ \\x=11[/tex]
2. By Angle Addition Postulate,
[tex]m\angle FED=m\angle DEB+m\angle BEF[/tex]
Since
[tex]m\angle FED=14x+8\\ \\m\angle DEB=22^{\circ}\\ \\m\angle BEF=13x-3,[/tex]
then
[tex]14x+8=22+13x-3\\ \\14x-13x=22-3-8\\ \\x=11[/tex]
Therefore,
[tex]m\angle BEF=(13\cdot 11-3)^{\circ}=(143-3)^{\circ}=140^{\circ}[/tex]
3. The area of trapezoid is
[tex]A_{trapezoid}=\text{Midsegment}\times \text{Height}[/tex]
From the diagram,
[tex]\text{Smaller base}=1.2\ in\\ \\\text{Bigger base}=4.2\ in,[/tex]
then
[tex]\text{Midsegment}=\dfrac{1.2+4.2}{2}=2.7\ in[/tex]
Since the area of trapezoid is [tex]11.6\ in^2,[/tex] then
[tex]11.6\ in^2 =2.7\ in\times \text{Height}\\ \\\text{Height}=\dfrac{11.6\ in^2}{2.7\ in}\approx 4.3\ in[/tex]
4. Use formula for the area of the circle to find the radius of the circle:
[tex]A_{circle}=\pi r^2[/tex]
So,
[tex]132.7=\pi r^2\\ \\r^2=\dfrac{132.7}{\pi}\\ \\r=\sqrt{\dfrac{132.7}{\pi}}\ ft[/tex]
Now, find the circumference of the circle:
[tex]C=2\pi r\\ \\C=2\pi \cdot \sqrt{\dfrac{132.7}{\pi}}=2\sqrt{132.7\pi}\approx 40.8\ ft[/tex]
