the sum of two adjacent angle is 80°the larger angle is 8°less than 3 tines the smaller find the number of degrees in each angle
Let x = smaller angle, then larger = 3x-8º.
x + (3x-8º) = 80º
Solve for x.
x=22; 3x-8=58
To solve this problem, let's first assign variables to the two angles. Let's say the smaller angle is x degrees.
According to the problem, the sum of the two adjacent angles is 80°. This means we can set up an equation:
x + (x + 8) = 80
Since the larger angle is 8° less than 3 times the smaller angle, we can express the larger angle as (3x - 8).
Now, let's solve the equation:
2x + 8 = 80 (combining like terms)
2x = 72 (subtracting 8 from both sides)
x = 36 (dividing both sides by 2)
So the smaller angle is 36°.
Now, we can find the larger angle by substituting the value of x into (3x - 8):
larger angle = 3(36) - 8
= 108 - 8
= 100°
Therefore, the smaller angle is 36° and the larger angle is 100°.