Question

Will give 100 points

Answer 1

The answer is <ACD = 68°

Explanation:

Using the property that the sum of interior angles in a triangle is equal 180°,we have:

<DAC + <ACD + <ADC = 180°

`2x + (180 - 4x) + 56 = 180 \\ - 2x + 56 = 0 \\ 2x = 56 \\ x = (56)/(2 ) \\ x = 28`

Finally, calculating the angle <ACD, we have:

<ACD = 180 - 4x

<ACD = 180 - 4 . 28

<ACD = 180 - 112

ACD = 68°

Answer 2

x = 28°

m∠ACD = 68°

Explanation:

From inspection of the given diagram:

• m∠FDC = 124°
• m∠EAB = 2x
• m∠ACG = 4x

Vertical Angle Theorem

When two straight lines intersect, the vertical angles are congruent.

⇒ m∠DAC = m∠EAB = 2x

Angles on a straight line sum to 180°:

⇒ m∠ACD + 4x = 180°

⇒ m∠ACD + 4x - 4x = 180° - 4x

⇒ m∠ACD = 180° - 4x

Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

⇒ m∠DAC + m∠ACD = m∠FDC

⇒ 2x + (180° - 4x) = 124°

⇒ -2x + 180° = 124°

⇒ -2x + 180° - 180° = 124° - 180°

⇒ -2x = -56°

⇒ -2x ÷ -2 = -56° ÷ -2

⇒ x = 28°

To find m∠ACD, substitute the found value of x into the expression for the angle:

⇒ m∠ACD = 180° - 4x

⇒ m∠ACD = 180° - 4(28°)

⇒ m∠ACD = 180° - 112°

⇒ m∠ACD = 68°