The measure of one base angle in an isosceles triangle is 20 degrees. The measure of the largest angle in the triangle is
A) 20 degrees
B) 90 degrees
C) 140 degrees
D) 160 degrees
To find the measure of the largest angle in an isosceles triangle, we need to know that the sum of all angles in a triangle is 180 degrees.
In an isosceles triangle, the base angles are congruent. Let's call each base angle x.
We know that x + x + largest angle = 180 degrees (sum of all angles in a triangle)
Therefore, 2x + largest angle = 180 degrees.
Given that one base angle is 20 degrees, we can substitute this value into the equation:
2(20 degrees) + largest angle = 180 degrees.
Simplifying the equation:
40 degrees + largest angle = 180 degrees.
To isolate the largest angle, we subtract 40 degrees from both sides of the equation:
largest angle = 180 degrees - 40 degrees.
Calculating:
largest angle = 140 degrees.
Therefore, the measure of the largest angle in the triangle is 140 degrees.
The correct answer is C) 140 degrees.
To find the measure of the largest angle in an isosceles triangle, we first need to know that an isosceles triangle has two equal sides. In such a triangle, the two base angles (the angles opposite to the equal sides) are equal.
Given that one base angle in the isosceles triangle is 20 degrees, we can conclude that the other base angle is also 20 degrees. This is because in an isosceles triangle, the base angles are always congruent.
Now, let's find the measure of the largest angle in the triangle. We know that the sum of the angles in any triangle is always 180 degrees. In an isosceles triangle, the two base angles are equal, so we can represent each base angle as "x."
Since the sum of the angles in the triangle is 180 degrees, we can set up the equation:
x + x + largest angle = 180
Since we know that each base angle is 20 degrees, we can substitute "x" with 20:
20 + 20 + largest angle = 180
Simplifying the equation:
40 + largest angle = 180
Now, solve for the largest angle:
largest angle = 180 - 40 = 140 degrees
Therefore, the measure of the largest angle in the triangle is 140 degrees.
The correct answer is C) 140 degrees.
the other base angle is also 20
since the three add to 180, ...