Question

find the value of x.
diagram: vertical line with points a (top), d (middle), c (bottom); ray db from d to b (right), forming angles (2x)° (between da and db) and (4x − 6)° (between dc and db).
x = \square

Explanation:

Answer:

Since \( \angle ADB = 2x^\circ \) and \( \angle CDB = (4x - 6)^\circ \) form a linear pair (they are adjacent angles on a straight line \( AC \)), their sum is \( 180^\circ \). So we set up the equation:

\[
2x + (4x - 6) = 180
\]

Combining like terms:

\[
6x - 6 = 180
\]

Adding 6 to both sides:

\[
6x = 186
\]

Dividing both sides by 6:

\[
x = 31
\]

So the value of \( x \) is \( 31 \).