In the diagram below, B, C, and D are all on the same line, angle BAC =24 degrees and AB = AC = CD
If angle ADC = x degrees, what is the value of x?
The sum of the angles in every triangle = 180° , so
∠ABC + ∠ACB + 24° = 180°
AB = AC , so triangle ABC is isoscelese and ∠ABC = ∠ACB .
∠ACB + ∠ACB + 24° = 180° Subtract 24 from both sides.
∠ACB + ∠ACB = 156° Combine like terms.
2∠ACB = 156° Divide both sides of the equation by 2 .
∠ACB = 78°
Since B, C, and D are on the same line...
∠ACB + ∠ACD = 180°
78° + ∠ACD = 180°
∠ACD = 102°
And triangle ACD is also isoscelese with ∠CAD = ∠ADC = x So...
x + x + 102° = 180°
2x = 78°
x = 39°
The sum of the angles in every triangle = 180° , so
∠ABC + ∠ACB + 24° = 180°
AB = AC , so triangle ABC is isoscelese and ∠ABC = ∠ACB .
∠ACB + ∠ACB + 24° = 180° Subtract 24 from both sides.
∠ACB + ∠ACB = 156° Combine like terms.
2∠ACB = 156° Divide both sides of the equation by 2 .
∠ACB = 78°
Since B, C, and D are on the same line...
∠ACB + ∠ACD = 180°
78° + ∠ACD = 180°
∠ACD = 102°
And triangle ACD is also isoscelese with ∠CAD = ∠ADC = x So...
x + x + 102° = 180°
2x = 78°
x = 39°