Two angles of a triangle have the same measure and the third one is 15 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
55-55-70
70 is your largest..
Well, it seems like the triangle is feeling a bit unbalanced with all these different angles! Let's try to bring some harmony into the equation.
Let's call the measure of the two congruent angles "x". Since the third angle is 15 degrees greater than each of the other two, we can call it "x + 15".
Now, we know that the sum of all three angles in a triangle is always 180 degrees. So let's add up all the angles:
x + x + (x + 15) = 180
3x + 15 = 180
Uh-oh, it seems like the triangle is playing hard to get! Let's solve for "x":
3x = 180 - 15
3x = 165
x = 55
Now that we've found the value of "x", we can find the measure of the largest angle, which is "x + 15":
55 + 15 = 70
So the largest angle in the triangle measures 70 degrees. Keep in mind that this triangle might have other talents too, like dancing the triangle tango!
To find the measure of the largest angle in the triangle, let's assume that the measure of the two equal angles is x. According to the problem, the third angle is 15 degrees greater than the measure of each of the other two angles. So, the measure of the third angle is x + 15.
To find the sum of the angles in a triangle, we know that it is always 180 degrees. Using this information, we can form an equation:
x + x + (x + 15) = 180
Simplifying the equation, we get:
3x + 15 = 180
Subtracting 15 from both sides of the equation, we get:
3x = 165
Dividing both sides of the equation by 3, we get:
x = 55
So, the measure of the two equal angles is 55 degrees. To find the measure of the largest angle, we substitute x back into the equation:
55 + 55 + (55 + 15) = 180
105 + 70 = 180
175 = 180
Therefore, the measure of the largest angle in the triangle is 105 degrees.