Given:
and
are vertical angles

Prove:
Two lines AC and DE intersect each other at a point B. The vertical angles CBD and ABE measures x plus 10 degrees and 2x plus 6 degrees.

A flow chart has 5 boxes. Moving left to right, boxes are labeled as follows, angles ABE and DBC are vertical angles, angle ABE congruent to angle DBC. The measure of angle ABE = measure of angle DBC. 2x plus 6 = x plus 10. x = 4.

Convert the flow chart proof into a paragraph proof.

It is given that
and
are vertical angles. By the
,
is congruent to
. By the definition of congruence, the measure of
must equal the measure of
. Then, by the substitution property of equality,
. Applying the subtraction property of equality gives
.