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Hitman42 [59]
3 years ago
7

Find the measure of 45. *5 = [?]

Mathematics
1 answer:
iragen [17]3 years ago
8 0

Answer:

angle7 = 80 (because vertically opposite angles are always equal)

angle7 + angle5 = 180 (because is a straight line)

80 + angle5 = 180

angle5 = 180 - 80

angle5 = 100

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Find the area of the trapezoid below to the nearest tenth.
kondor19780726 [428]

Answer:

Area of trapezoid = 67.6 square units

Step-by-step explanation:

Area of a trapezoid is given by the expression,

Area of the trapezoid = \frac{1}{2}(b_1+b_2)h

Here, b_1 and b_2 are the parallel sides of the given trapezoid.

And 'h' = Height between the parallel sides

From the given triangle ABE,

m(∠ABE) = m(∠ABC) - m(∠EBC)

m(∠ABE) = 120° - 90°

               = 30°

By applying cosine rule in the given triangle,

cos(30°) = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

\frac{\sqrt{3} }{2}=\frac{BE}{AB}

\frac{\sqrt{3} }{2}=\frac{BE}{6}

BE = 3\sqrt{3} units

By applying sine rule in ΔABE,

sin(30°) = \frac{\text{Opposite side}}{\text{Hypotenuse}}

\frac{1}{2}=\frac{AE}{AB}

\frac{1}{2}=\frac{AE}{6}

AE = 3 units

Length of b_1=BC=10

Length of b_2=AD=(AE+EF+FD) [AE = FD, since given trapezoid ABCD is an isosceles trapezoid]

                b_2=3+10+3

                b_2=16

Height between the parallel sides h=3\sqrt{3}

Area of the trapezoid = \frac{1}{2}(BC+AD)BE

                                    = \frac{1}{2}(10+16)(3\sqrt{3})

                                    = 39\sqrt{3}

                                    = 67.6 square units

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