ABCd is a pentagon made up of five equal sides and 5 equal interior angles.BE is a diagonal forming a house . Angle B is split into a and t. E is split into E1 and E2. Calculate the interior angles.?

Since ABCd is a pentagon with equal sides and equal interior angles, each interior angle of the pentagon is 108 degrees (since the sum of interior angles of a pentagon is 540 degrees).

Since BE is a diagonal of the pentagon, it divides angle B into two equal angles, a and t. Therefore, angle B is split into two angles of 54 degrees each.

Similarly, since E is a diagonal of the pentagon, it divides angle E into two equal angles, E1 and E2. Therefore, angle E is split into two angles of 54 degrees each.

Therefore, the interior angles of the pentagon ABCd are:
- Angle A = 108 degrees
- Angle B = 54 degrees
- Angle C = 108 degrees
- Angle d = 108 degrees
- Angle E = 54 degrees

Step 1: Interior Angles of a Pentagon

- A regular pentagon has 5 equal sides and 5 equal interior angles.
- The sum of the interior angles of a polygon with n sides is (n-2) - 180°.
- For a pentagon, this is (5-2) - 180° = 540°.

Step 2: Interior Angles of the House

- Angle B is split into two angles, a and t.
- Since the interior angles of a pentagon are equal, we know that:
- m∠a = m∠t = m∠E1 = m∠E2 = x

Step 3: Angle at Point E

- The interior angles of a polygon at a vertex must sum to 360°.
- Therefore, we have:
- m∠E + m∠E1 + m∠E2 = 360°
- m∠E + x + x = 360°
- m∠E = 360° - 2x

Step 4: Interior Angles of the Pentagon

- We now have three unknown angles to solve for: x, a, and t.
- Since x is shared between the house and the pentagon, we can use the fact that the sum of the interior angles of the pentagon is 540°:
- m∠a + m∠t + m∠E + m∠B + m∠C + m∠D = 540°
- x + x + (360° - 2x) + 180° + 180° + 180° = 540°
- 4x = 360°
- x = 90°

Step 5: Interior Angles of the House

- Now that we know x = 90°, we can find the interior angles of the house:
- m∠a = m∠t = 90°
- m∠E = 360° - 2x = 360° - 2(90°) = 180°

Therefore, the interior angles of the pentagon are:

- m∠A = m∠B = m∠C = m∠D = 180°
- m∠E = 180°

And the interior angles of the house are:

- m∠a = m∠t = 90°
- m∠E = 180°