Question

If m∠ABC + m∠CBD = 90, m∠ABC = 3x – 5, and m∠CBD = 2x + 62, then x = _____ .

Answer 1

To solve for x, we set up the equation 3x - 5 + 2x + 62 = 90, combine like terms to get 5x + 57 = 90, solve for x by subtracting 57 from both sides to get 5x = 33, and then divide both sides by 5 resulting in x = 6.6.

Step-by-step explanation:

To find the value of x given that m∠ABC + m∠CBD = 90, we substitute the given expressions for m∠ABC (3x – 5) and m∠CBD (2x + 62) into the equation.

Therefore, we have:

1. 3x – 5 + 2x + 62 = 90
2. 5x + 57 = 90
3. 5x = 90 – 57
4. 5x = 33
5. x = 33 / 5
6. x = 6.6

The value of x is 6.6.