Answer:
The third angle is:
2x−16=2×49−16=82.
Explanation:
. The third angle is given as 16 degrees less than the sum of the two equal angles, so it can be represented as 2x−16
.
The sum of all angles in a triangle is 180 degrees. Therefore, we can set up the following equation:
2x+(2x−16)=180
Solving this equation will give us the value of x
, which represents the two equal angles, and 2x−16
, which represents the third angle. Let’s solve it:
First, simplify the equation:
4x−16=180 Next, add 16 to both sides of the equation:
4x=196
Finally, divide both sides of the equation by 4 to solve for x
:
x=49 the two equal angles are each 49 degrees. The third angle is:
2x−16=2×49−16=82.