the first angle of a triangle is complementry to the third angle.
the second angle is 16 degrees less than five times the first angle.
find the measure of the largest angle of the triangle.
x = 1st angle
90 - x = 2nd angle
5x - 16 = 3rd angle
x + 90 - x + 5x - 16 = 180
solve for x
x=21.2
To find the measure of the largest angle of the triangle, let's represent the first angle as "x". Since the first angle is complementary to the third angle, the third angle can be represented as "90 - x".
The second angle is 16 degrees less than five times the first angle, which can be represented as "5x - 16".
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
x + (90 - x) + (5x - 16) = 180
Now let's solve for x:
Combining like terms, we have:
x + 90 - x + 5x - 16 = 180
5x + 74 - x = 180
4x + 74 = 180
Subtracting 74 from both sides, we have:
4x = 106
Dividing both sides by 4, we get:
x = 26.5
So, the value of x (the first angle) is 26.5 degrees.
To find the measure of the largest angle, we substitute the value of x into the expression for the third angle:
Third angle = 90 - x = 90 - 26.5 = 63.5 degrees
Therefore, the measure of the largest angle in the triangle is 63.5 degrees.