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Ludmilka [50]
2 years ago
11

If someone could please help me I’m confused thanks:)

Mathematics
1 answer:
Sedbober [7]2 years ago
3 0
<h3>Answer:  x = 45</h3>

Work Shown:

x+x+90 = 180 .... all three angles of a triangle add to 180

2x+90 = 180

2x = 180-90

2x = 90

x = 90/2

x = 45

This is a 45-45-90 right triangle. We also consider it an isosceles right triangle because the base angles (45) are equal.

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3 years ago
Find the perimeter of the polygon with vertices A(-6,-4), B(-3,6), C(4,0), and D(2,-1)?
EleoNora [17]
Check the picture below.

so the perimeter of the polygon is the sum of all its sides, namely, AB + BC + CD + DA.

now, let's check how long each side is,

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&A&(~{{ -6}} &,&{{ -4}}~) &#10;%  (c,d)&#10;&B&(~{{ -3}} &,&{{ 6}}~)&#10;\end{array}&#10;\\\\\\&#10;d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\&#10;-------------------------------\\\\&#10;AB=\sqrt{[-3-(-6)]^2+[6-(-4)]^2}&#10;\\\\\\&#10;AB=\sqrt{(-3+6)^2+(6+4)^2}&#10;\\\\\\&#10;AB=\sqrt{3^2+10^2}\implies \boxed{AB=\sqrt{109}}\\\\&#10;-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&B&(~{{ -3}} &,&{{6}}~) &#10;%  (c,d)&#10;&C&(~{{ 4}} &,&{{ 0}}~)&#10;\end{array}&#10;\\\\&#10;-------------------------------\\\\&#10;BC=\sqrt{[4-(-3)]^2+[0-6]^2}\implies BC=\sqrt{(4+3)^2+(0-6)^2}&#10;\\\\\\&#10;BC=\sqrt{7^2+(-6)^2}\implies \boxed{BC=\sqrt{85}}\\\\&#10;-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&C&(~{{ 4}} &,&{{0}}~) &#10;%  (c,d)&#10;&D&(~{{ 2}} &,&{{ -1}}~)&#10;\end{array}&#10;\\\\&#10;-------------------------------\\\\&#10;CD=\sqrt{(2-4)^2+(-1-0)^2}\implies CD=\sqrt{(-2)^2+(-1)^2}&#10;\\\\\\&#10;\boxed{CD=\sqrt{5}}\\\\&#10;-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&D(~{{ 2}} &,&{{-1}}~) &#10;%  (c,d)&#10;&A&(~{{ -6}} &,&{{ -4}}~)&#10;\end{array}\\\\&#10;-------------------------------\\\\&#10;DA=\sqrt{[-6-2]^2+[-4-(-1)]^2}\\\\\\ DA=\sqrt{(-6-2)^2+(-4+1)^2}&#10;\\\\\\&#10;DA=\sqrt{(-8)^2+(-3)^2}\implies \boxed{DA=\sqrt{73}}

sum those sides up, and that's the perimeter of the polygon.

6 0
2 years ago
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