Certainly! Let's solve this problem step by step.
1. Understand the problem statement:
We are given a triangle with one angle measuring 80°, and we are told that the other two angles are equal.
2. Recall the property of angles in a triangle:
The sum of the interior angles of any triangle is always 180°.
3. Set up an equation:
Since one angle is given as 80°, let's denote each of the equal angles by [tex]\( x \)[/tex]. Therefore, we have:
[tex]\[
80° + x + x = 180°
\][/tex]
4. Combine like terms:
Simplify the equation by combining the [tex]\( x \)[/tex] terms together:
[tex]\[
80° + 2x = 180°
\][/tex]
5. Isolate [tex]\( x \)[/tex]:
To find the value of [tex]\( x \)[/tex], subtract 80° from both sides of the equation:
[tex]\[
2x = 180° - 80°
\][/tex]
[tex]\[
2x = 100°
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
Now, divide both sides of the equation by 2:
[tex]\[
x = \frac{100°}{2}
\][/tex]
[tex]\[
x = 50°
\][/tex]
7. Conclusion:
The measure of each of the equal angles is 50°.
So, the two equal angles in the triangle each measure 50°.
