CBD = 38°
ABD = 19°
Explanation:
CBD = (3x + 23)°
ABC = 123°
ABD = (x + 14)°
We know that the angles in a triangle add up to 180°. So, we can set up an equation using these angles:
ABC + ABD + CBD = 180°
Now, plug in the values we have:
123° + (x + 14)° + (3x + 23)° = 180°
Combine like terms:
123° + x + 14 + 3x + 23 = 180°
Combine constants:
160° + 4x = 180°
Subtract 160° from both sides:
4x = 20°
Now, divide by 4 to isolate x:
x = 5°
Now that we have found the value of x, we can find the measurements of CBD and ABD:
CBD = 3x + 23°
CBD = 3(5°) + 23°
CBD = 15° + 23°
CBD = 38°
ABD = x + 14°
ABD = 5° + 14°
ABD = 19°