Answer: 4) x° = 33.5°
5) x° = 31°
Step-by-step explanation: 4) It is supplementary i.e. the angle add up to 180° .
(4x+5)° +41° = 180°
4x+46 = 180°
4x = 180-46 = 134
4x = 134/4 = 33.5°
5) It is complementary i.e. angles add up to 90°
x°+(2x-3)° = 90°
3x - 3 = 90
3x = 93
x = 31°
Problem 1
<h3>Answers:</h3><h3>angle 6 = 50</h3><h3>angle 7 = 50</h3><h3>angle 8 = 40</h3>
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Work Shown:
point E = intersection point of diagonals.
x = measure of angle 6
y = measure of angle 8
angle 7 is also x because triangle AED is isosceles (AE = ED)
Focus on triangle AED, the three angles A, E, D add to 180
A+E+D = 180
x+80+x = 180
2x+80 = 180
2x = 180-80
2x = 100
x = 100/2
x = 50
So both angles 6 and 7 are 50 degrees.
Turn to angle 8. This is adjacent to angle 7. The two angles form a 90 degree angle at point A. This is because a rectangle has 4 right angles.
(angle7)+(angle8) = 90
50+y = 90
y = 90-50
y = 40
angle 8 = 40 degrees
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Problem 2
<h3>Answers:</h3><h3>angle 2 = 61</h3><h3>angle 3 = 61</h3>
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Work Shown:
Angle 5 is 29 degrees (given). So is angle 4 because these are the base angles of isosceles triangle DEC (segment DE = segment EC)
angle 3 and angle 4 form a 90 degree angle
x = measure of angle 3
(angle 3)+(angle 4) = 90
x+29 = 90
x = 90-29
x = 61
Angle 2 is congruent to angle 3 since triangle BEC is isosceles (BE = EC), so both angle 2 and angle 3 are 61 degrees each.
G is<span> the centroid it means that BG/FG=2 (G divides the median with this ratio)
3x+6/2x-1=2
3x+6=4x-2
x=8
then AG=26 then GE=13 so AE=39</span>
Your answer is going to be <span>3x=1.</span>
