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matrenka [14]
2 years ago
13

Lamar wanted to explain why the measure of angle 5 is equal to the sum of the measures of angles 1 and 3. A triangle with angles

1, 2, 3. The exterior angle to angle 1 is 4, to 2 is 5, to 3 is 6. Which geometry concepts should be used in Lamar’s work? supplementary angles and the sum of the measures of interior angles of a triangle complementary angles and the sum of the measures of interior angles of a triangle supplementary angles and vertical angles the sum of the measures of interior angles of a triangle and vertical angles.
Mathematics
1 answer:
Sati [7]2 years ago
8 0

Lamar explains it correctly. Then the angle ∠5 is equal to the sum of angles ∠1 and ∠2.

<h3>What is an angle?</h3>

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Lamar wanted to explain why the measure of angle 5 is equal to the sum of the measures of angles 1 and 3.

A triangle with angles 1, 2, 3. The exterior angle to angle 1 is 4, to 2 is 5, to 3 is 6.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

∠2 + ∠5 = 180° ...1

Triangle - The sum of the angle of the triangle is 180 degrees.

∠1 + ∠2 + ∠3 = 180° ...2

From equations 1 and 2, we have

∠2 + ∠5 = ∠1 + ∠2 + ∠3

        ∠5 = ∠1 + ∠3

Thus, angle ∠5 is equal to the sum of angles ∠1 and ∠2.

More about the angled link is given below.

brainly.com/question/15767203

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Answer:

<u>Volume</u>

For the rectangle, h = 3cm, l = 8cm, w = 6cm
V = length x width x height
V = 8cm x 6cm x 3cm
V = 144cm^3

For the semi circle, we need to find the radius. The radius is width/2, so 6cm/2 = 3cm. r = 3cm, \pi = 3.14
V = radius^2 x height x \pi
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V = 84.8 cm^3/2 (because the cylinder needs to be divided to form a semi-circle)
V= 42.4cm^3 (there are two cylinders though so we will multiply this by 2 in the total volume)

Total volume:
V = 144cm^3 + 42.4cm^3(2)
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Rectangular prism:
A = 2[w(l) + h(l) + h(w)]
A = 2[6cm(8cm) + 3cm(8cm) + 3cm(6cm)]
A = 180cm^2
But there are two sides that are covered by the semi-circular prisms, so we will have to calculate those sides and remove them.
A = l x w
A = 6cm x 3cm
A = 18cm^2(2) (2 being the two faces)
A = 36cm^2

A = 180cm^2 - 36cm^2
A = 144cm^2 (the area of the rectangle)

Semi-circular prism:
A = 2\pirh + 2\pir^2
Earlier, we found out that the radius of the circle is 3cm, so we will plug that in.
A = 2(3.14)(3cm)(3cm) + 2(3.14)(3cm)^2
A = 113.09cm^2

Total surface area:
A = 144cm^2 + 133.09cm^2
A = 277.09cm^2

Therefore the total volume of the prism is 186.4cm^3 and the total surface area is 277.09cm^2.





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