memoryofdale
12.11.2020 •
Mathematics
In quadrilateral ABCD, \angle A=5x+20,\angle B=3x-30,\angle C=2x+10,and\angle D=8x.∠A=5x+20,∠B=3x−30,∠C=2x+10,and∠D=8x. Find the value of Angle B.
Equation:
x=
angle b=
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Ответ:
Equation: (5x + 20) + (3x - 30) + (2x + 10) + 8x = 360
x = 20
Angle B = 30°
Step-by-step explanation:
Given:
<A = 5x + 20
<B = 3x - 30
<C = 2x + 10
<D = 8x
Sum of interior angles of a quadrilateral = 360°
Therefore:
<A + <B + <C + <D = 360°
(5x + 20) + (3x - 30) + (2x + 10) + 8x = 360
Solve for x
5x + 20 + 3x - 30 + 2x + 10 + 8x = 360
Collect like terms
5x + 3x + 2x + 8x + 20 - 30 + 10 = 360
18x = 360
Divide both sides by 18
x = 360/18
x = 20
<B = 3x - 30
Plug in the value of x
<B = 3(20) - 30 = 60 - 30
<B = 30°
Ответ:
9-10x≥0
-10x≥-9
x≤9/10
{x|x≤-10}