Question

24 points !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

x = 58°

y = 15°

Explanation:

Angle DAE = 180 - 72 - 50

= 58

Angle BAC = Angle DAE

(Vertically opposite angles)

x = 58°

Angle DAC = 180/3 = 60

(Equilateral triangle)

60 = 2y + 2y

Exterior angle = sum of interior

60 = 4y

y = 15°

Answer 2

x = 58 and y = 15

Explanation:

(c)

The sum of the 3 angles in a triangle = 180°

In Δ ADE

∠ DAE = 180° - (50 + 72)° = 180° - 122° = 58°

∠ DAE and ∠ CAB are vertical and congruent, thus

x = 58

(d)

Δ ACD is equilateral thus all 3 angles = 60°

∠ CAB and ∠ CAD are adjacent and supplementary, thus

∠ CAB = 180° - 60° = 120°

Since CA = BA then Δ ABC is isosceles with base angles congruent, thus

2y + 2y = 60

4y = 60 ( divide both sides by 4 )

y = 15