Sure! Let's solve this step by step.
1. Determine the Sum of the Interior Angles of a Pentagon:
- A pentagon has 5 sides.
- The sum of the interior angles of a polygon with [tex]\( n \)[/tex] sides is given by the formula:
[tex]\[
(n-2) \times 180^\circ
\][/tex]
- For a pentagon ([tex]\( n = 5 \)[/tex]):
[tex]\[
(5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\][/tex]
2. Sum of the Known Angles:
- You are given two angles: [tex]\( 98^\circ \)[/tex] and [tex]\( 118^\circ \)[/tex].
- Sum of these two angles:
[tex]\[
98^\circ + 118^\circ = 216^\circ
\][/tex]
3. Sum of the Remaining Three Equal Angles:
- Since the sum of all interior angles is [tex]\( 540^\circ \)[/tex] and we already know that two of the angles sum up to [tex]\( 216^\circ \)[/tex]:
[tex]\[
\text{Sum of the remaining three angles} = 540^\circ - 216^\circ = 324^\circ
\][/tex]
4. Calculate Each of the Three Equal Angles:
- Since the remaining three angles are equal, each of the three equal angles will be:
[tex]\[
\frac{324^\circ}{3} = 108^\circ
\][/tex]
Therefore, the remaining three equal angles in the pentagon are each [tex]\( 108^\circ \)[/tex].
