Find the measure of angle x in the figure below:

Solution:

From the given figure, clearly ∠BAD, ∠BAC and ∠CAE are angles on line DE and therefore they sum to 180°.

∴ ∠BAD + ∠BAC + ∠CAE = 180°

56° + y + 51° = 180°

y = 73°

We know that the sum of angles of a triangle is 180°.

Here, the sum of angles of triangle ABC = 180°

⇒ x + y + 72° = 180°

x + 73° + 72° = 180°

x = 35°

Find the measure of angle x in the figure below:

Summary:

The measure of angle x in the figure is 35°.