Question

E is a point on side BC of the square ABCD, ∠AEB = 55°. find ∠EAC.

पर्याय

• 35°

• 25°

• 10°

• 15°

Answer 1

10°

Explanation:

Step 1: Use the properties of a square

In a square ABCD, all interior angles are 90°.

The diagonal AC bisects the angle at the vertex A,

So `∠BAC = 1/2 ∠DAB`

= `1/2 (90^circ)`

= 45°

Step 2: Find angle BAE

Consider the right-angled triangle ΔABE.

Since E is on side BC, ∠ABE = ∠ABC = 90°.

The sum of angles in a triangle is 180°.

We are given ∠AEB = 55°.

We can find ∠BAE using this information.

∠BAE + ∠ABE + ∠AEB = 180°

∠BAE + 90° + 55° = 180°

∠BAE + 145° = 180°

∠BAE = 180° – 145°

∠BAE = 35°

Step 3: Solve for angle EAC

The angle ∠EAC can be found by subtracting ∠BAE from the total angle ∠BAC.

∠EAC = ∠BAC – ∠BAE

∠EAC = 45° – 35°

∠EAC = 10°