33.7k views
3 votes
If CBD = (3x + 23)°, ABC=123 and ABD = (× + 14). Find the measurements of CBD and ABD

User Frank Hu
by
7.9k points

1 Answer

4 votes

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°

User Natim
by
8.4k points

Related questions

1 answer
2 votes
140k views
1 answer
5 votes
15.7k views
1 answer
4 votes
48.1k views