Question

Can you please solve this?

Answer 1

Answer:

Step-by-step explanation:

- (1) Diagonals of a square are angels' bisectors;

- (2) Diagonals of a square are perpendicular bisectors;

- (3) Alternate exterior angles are congruent;

- (4) Supplementary angles are either of two angles whose sum is 180°;

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4.(a).

Δ AED :

m∠DAE = 90° ÷ 2 = 45° (reason (1))

m∠AED = 180° - 82° = 98° (reason (2))

a° = 180° - (98° + 45°) = 37°

∠EDC ≅ ∠EFA (reason (3))

m∠EFA = 90° - 37° = 53°

b° = 180° - 53° = 127°

4. (b).

Δ FEC :

m∠ FCE = 45° (r. (1))

2c° + 45° = 180° ⇒ c° = 67.5°

d° + c° = 90° ⇒ d° = 22.5°