Question

In the given diagram ⃤ ABC and ⃤ CDE are equilateral triangles. If ∠EBD = 62° then find the measure of 1/2 of ∠AEB.

Answer 1

Given

△ABC and △CDE are equilateral.

AE

= 25

To find perimeters of the two triangles,

Let us consider the lengths of

AC

and

CE

to be

′

x

′

and

′

y respectively.

As △ABC is equilateral,

AC

=

AB

=

BC

= x

As △CDE is equilateral,

CE

=

CD

=

DE

= y

From the figure,

AE

=

AC

+

CE

25 = x + y

x + y = 25

Perimeter of the triangle is the sum of all sides of the triangle.

For △ABC,

Perimeter of △ABC =

AC

+

AB

+

BC

= x + x + x

= 3x

For △CDE,

Perimeter of △CDE =

CE

+

CD

+

DE

= y + y + y

= 3y

Now,

Perimeter of two triangles = Perimeter of △ABC + Perimeter of △CDE

= 3x + 3y

= 3 × (x + y)

= 3 × 25 (from above)

= 75

Therefore, Perimeter of the two triangles is'75′units.

Explanation:

Hope it is helpful...

Answer 2

The measure of 1/2 of ∠AEB is 31°.

In the given diagram, ⃤ ABC and ⃤ CDE are equilateral triangles. Since all angles of an equilateral triangle measure 60°, we have:

∠ABC = ∠ACB = ∠BAC = 60°

∠CDE = ∠CED = ∠EDC = 60°

We are also given that ∠EBD = 62°. Since ∠EBD and ∠ABC share a common side, they are supplementary angles. This means that ∠EBD + ∠ABC = 180°. Therefore:

∠ABC = 180° - ∠EBD = 180° - 62° = 118°

Now, let's consider ∠AEB. Since ∠ABC and ∠AEB are exterior angles of ⃤ CDE, they are supplementary angles. This means that ∠ABC + ∠AEB = 180°. Therefore:

∠AEB = 180° - ∠ABC = 180° - 118° = 62°

Finally, we are asked to find the measure of 1/2 of ∠AEB. This is simply:

1/2 * ∠AEB = 1/2 * 62° = 31°

Therefore, the measure of 1/2 of ∠AEB is 31°.