One angle of an isosceles triangle measures 140°. which other angles could be in that isosceles triangle? choose all that apply.
70° 80° 30° 20° submit
1 answer:
Answer:
20°
<h2>Step-by-step explanation:</h2>An Isosceles triangle is a triangle having two sides with the same length. The general form of this type of triangles is shown in the figure marked as 1 below. As you can see, two sides are equals and they are represented by the harsh marks. Since two sides are equals, then there will be two equal angles as well. If one angle measures 140°, then there is only one possibility:
<h3>1. The given angle is opposite to the side where the two equal angles lies:</h3>This is the case of the figure marked as 2. Since the internal angles of a triangle add up to 180°, then it is true that:
2x + 140° = 180° ∴ 2x = 40° ∴ x = 20°
It's impossible that the given angle lies on one of the two equal angles as indicated in figure marked as 3, because in this case we'd have two angles that measure 140° each, but 140° + 140° is greater than 180°, so this is impossible for internal angles of a triangle.
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Greetings!
To start this problem, let's first assign a variable for the missing, consecutive odd numbers. Since they are consecutive and odd, we add two.
<u>Proof:</u> <em>3-1=2, 5-3=2</em>
The first, consecutive, odd number:
The second, consecutive, odd number:
The third, consecutive, odd number:
The fourth, consecutive, odd number:
The sum of the values are equal to 3 times the sum of the first two numbers, of which this is equal to 35 less than the fourth number. Let's create an equation to simplify this:
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If is equal to -7:
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I hope this helps!
-Benjamin