I'm not sure what to do on these questions.
The measure of the vertex angle of an isosceles triangle is 26. Find the measure of each base angle
If the measures of the three angles of a triangle are x,2x-20, and 3x-10, then what is this type of triangle? Why?
1) By definition an icosceles triangle's two base angles are equal, so if you know all the angles add up to 180 then you subtract 26 from 180 and divide what's left by 2 to your answer.
2)X+2X-20+3X-10=180
X=35
Angles are 35, 50, 95
What kind of triangle is this?
You answer is at the following website:
http://www.mathwords.com/s/scalene_triangle.htm
For the first question, to find the measure of each base angle of an isosceles triangle, you can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.
Since the triangle is isosceles, it means that the vertex angle is equal to the base angles. Let's denote the measure of each base angle as "a".
We know that the measure of the vertex angle is 26 degrees.
To find the measure of each base angle, we can subtract the measure of the vertex angle from 180 and divide the result by 2.
So, the formula to find the measure of each base angle is:
a = (180 - 26) / 2
Simplifying the equation:
a = 154 / 2
a = 77
Therefore, the measure of each base angle in the isosceles triangle is 77 degrees.
For the second question, you need to determine the type of triangle based on the given angle measures.
The sum of the angles in any triangle is always 180 degrees. So, you can set up the equation using the angle measures given in the question:
x + (2x - 20) + (3x - 10) = 180
Simplifying the equation:
6x - 30 = 180
Adding 30 to both sides:
6x = 210
Dividing both sides by 6:
x = 35
Now that you have found the value of x, you can substitute it back into the original equation to find the measures of the three angles:
Angle 1: x = 35 degrees
Angle 2: 2x - 20 = 2(35) - 20 = 70 - 20 = 50 degrees
Angle 3: 3x - 10 = 3(35) - 10 = 105 - 10 = 95 degrees
Now, to determine the type of triangle, you can compare the three angles:
- If all three angles are equal, then the triangle is an equilateral triangle.
- If two angles are equal, but the third angle is different, then the triangle is an isosceles triangle.
- If all three angles are different, then the triangle is a scalene triangle.
In this case, the measures of the angles are 35, 50, and 95 degrees, which means all three angles are different. Therefore, the type of triangle is a scalene triangle.
Hope this helps!