Question

How much is the angle marked in the picture below?

Answer 1

From the figure, we can see that there are two set squares ABC and CDE.

We know that each acute angle in the set square ABC measures 45°, i.e., ∠ABC = ∠ACB = 45°.

Also, the measurements of each acute angle in the set square CDE are as follows:

∠DCE = 30° and ∠DEC = 60°

Again, from the figure, we can observe that ∠ACB and ∠ACE make a linear pair.

We know that the angles in a linear pair are supplementary.

∴ ∠ACB + ∠ACE = 180°

⇒ ∠ACB + (∠ACD + ∠DCE) = 180°

⇒ 45° + ∠ACD + 30° = 180°

⇒ ∠ACD + 75° = 180°

⇒ ∠ACD = 180° − 75° = 105°