Answer:
<u> x = 16</u>
Step-by-step explanation:
See the attched figure
We should know that, one of the properties of the rhombus is the diagonals bisect the angles of the rhombus.
Given:
m∠ABC = 84 and m∠ABE = 3x − 6
So, m∠ABE = 0.5 * m∠ABC = 0.5 * 84 = 42
∴ 3x - 6 = 42
Solve for x
3x = 42 + 6 = 48
x = 48/3 = 16
<u>∴ x = 16</u>
Answer:
69.81 sq. m. (rounded to 2 decimal places)
Step-by-step explanation:
The sector of a circle is "part" or "portion" of a circle. The formula for the area of a sector is:
Where
is the central angle
r is the radius
Given the figure, the arc is given as 80 degrees, but not the central angle of the shaded sector. But from geometry we know that the central angle and the intercepted arc have the same measure. So we can say:
Also, the radius of the circle shown is 10 meters, so
r = 10
Now, we substitute in formula and find our answer:
Thus,
The area of the shaded sector is 69.81 sq. meters.
