Question

Find the value of x in the expressions if A=2x+51 and B=7x−15 (right triangle)

Answer 1

In a right triangle, the sum of the angles is always 180 degrees, and one of the angles is 90 degrees. Therefore, if \( A \) and \( B \) are the two non-right angles of the triangle, we can use the following equation:

\[
A + B + 90 = 180
\]

This simplifies to:

\[
A + B = 90
\]

Now substitute the expressions for \( A \) and \( B \):

\[
(2x + 51) + (7x - 15) = 90
\]

Combine like terms:

\[
2x + 51 + 7x - 15 = 90
\]
\[
(2x + 7x) + (51 - 15) = 90
\]
\[
9x + 36 = 90
\]

Now, isolate \( x \) by first subtracting 36 from both sides:

\[
9x = 90 - 36
\]
\[
9x = 54
\]

Now, divide by 9:

\[
x = \frac{54}{9}
\]
\[
x = 6
\]

Thus, the value of \( x \) is \( \boxed{6} \).