Answer:
x = 122°
w = 90°
Step-by-step explanation:
x + 58° = 180°
[Sum of linear pair of angles measure 180°. If the pair is a set of two angles then the angles of this linear pair are called as Supplementary angles]
x = 180° - 58°
x = 122°
Similarly, w + 90° = 180°
w = 180° - 90°
w = 90°
Therefore, values of each variable are x = 122° and w = 90°.
Answer:
52
Step-by-step explanation:
If JK bisects the angle, the two angles are equal
6x+2 = 8x-6
Subtract 6x from each side
6x-6x+2 = 8x-6x-6
2 = 2x-6
Add 6 to each side
2+6 =2x-6+6
8 =2x
Divide by 2
8/2 =2x/2
4 =x
Now find angle LJM, which is the sum of the two angles
6x+2 + 8x-6
14x -4
14*4-4
56-4
52
<h3>
Answer: 192 square units</h3>
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Explanation:
Refer to the diagram below.
Draw a line through point D such that it is perpendicular to side BC. This new line intersects BC at point E.
In other words, E is on BC such that segments DE and BC are perpendicular.
Notice how triangle CED is a right triangle with legs DE and EC. The hypotenuse is DC = 16.
Let h be the height of the trapezoid. It's also the height of triangle CED where EC is the base. In other words, h = length of DE.
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Focus on triangle CED. We'll use the sine ratio to find h
sin(angle) = opposite/hypotenuse
sin(C) = DE/DC
sin(30) = h/16
0.5 = h/16
0.5*16 = h
8 = h
h = 8
The height of triangle CED is 8, so the height of the trapezoid is also 8.
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Apply the area of a trapezoid formula
Area = height*(base1+base2)/2
A = h*(b1+b2)/2
A = 8*(27+21)/2
A = 8(48)/2
A = 8*24
A = 192
The trapezoid's area is 192 square units
3/7*5=2.14285714.
15/7=2 1/7