To find the largest angle in the triangle with angle measures of (x−20)°, (3x+3)°, and (2x−7)°, we can set up an equation using the Triangle Angle Sum Theorem which states that the sum of the angles in a triangle is always 180 degrees.
(x−20) + (3x+3) + (2x−7) = 180
6x - 24 = 180
6x = 204
x = 34
Now, we can plug in the value of x into the angle measures to find the largest angle:
(34-20) = 14°
(3(34)+3) = 105°
(2(34)-7) = 61°
Therefore, the largest angle in the triangle is 105°.
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In the triangle with angles measuring 2x, 96 degrees, and x + 12 degrees, we can set up an equation using the Triangle Angle Sum Theorem again:
2x + 96 + x + 12 = 180
3x + 108 = 180
3x = 72
x = 24
Now we can find the smallest angle by plugging in the value of x:
24 + 12 = 36°
Therefore, the smallest angle of the triangle is 36 degrees.
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Given that two sides of the triangle are 10 mm and 7 mm, we can use the Triangle Inequality Theorem to find the possible range of the third side:
The third side must be greater than the difference of the two given sides and less than the sum of the two given sides.
7 - 10 < third side < 7 + 10
-3 < third side < 17
Therefore, the third side can be either 1 mm or 2 mm from the choices given.
Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)° , (3x+3)° , and (2x−7)° .(1 point)
Triangles Unit Test
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Question
Use the image to answer the question.
A triangle is shown with its angles measuring 2 x, 96 degrees, and x plus 12 degrees.
Find the measure of the smallest angle of the triangle.(1 point)
°
Two sides of a triangle are 10 mm and 7 mm. Determine the length of the third side from the choices given.(1 point)
Responses
1 mm
1 mm
20 mm
20 mm
2 mm
2 mm
5 mm
1 answer