Question

What is the measure of DAC in the image shown?

Answer 1

Answer: ∠DAC = 21
Explanation:
I would start with what I know in this case its going to be
2x + 113 + 2 - 15x = 180
we can use this equation to solve for x
x=-5
From there we can take our value of x which is -5 and substitute it where it belongs.
for example 1 - 4 (-5) = 21
I hope this helps!

Answer 2

m∠DAC = 21°

Explanation:

Exterior Angle Theorem

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

Apply the Exterior Angle Theorem to triangle ACD and solve for x:

⇒ m∠DAC + m∠ACD = m∠ACH

⇒ (1 - 4x) + (2 - 15x) = 2x + 108

⇒ -4x - 15x + 1 + 2 = 2x + 108

⇒ -19x + 3 = 2x + 108

⇒ -19x + 3 = 2x + 108

⇒ -21x + 3 = 108

⇒ -21x = 105

⇒ x = -5

Substitute the found value of x into the expression for angle DAC:

⇒ m∠DAC = 1 - 4x

⇒ m∠DAC = 1 - 4(-5)

⇒ m∠DAC = 1 + 20

⇒ m∠DAC = 21°

Therefore, the measure of angle DAC is 21°.