In the figure, angle I measures 56° and angle A measures 38° The measurement of angle B is The measurement of angle C is The measurement of angle F is

To find the measure angles B, C and F, you will need to know that the sum of all the angles in a triangle total 180 degrees and the sum of all the angles in a quadrilateral equal 360 degrees.

1.  Start with what you know:  angles I, E, and H needs to equal 180 (it is a straight line).  180 - 56 - 90 = 34 degrees.

H = 34 degrees

2.  Angles H, G, and A must equal 180, so 180-34-38 = 108 degrees

G = 108 degrees.

3.  Angles G and F must equal 180 degrees (straight line), so 180-108 = 72

F = 72 degrees

4.  Angles E, D, F, and C must equal 360, so 360-180-72 = 108

C = 108 degrees

5.  Angles J and D must add up to 180 (straight line); so 180-90=90

J = 90 degrees

6.  Angles B, I, and J must add up to 180, so 180-56-90=34

B = 34 degrees

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

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step-by-step explanation: