Question

In a pentagon ABCDE, side AB is parallel to side ED and ∠B:∠C:∠D is 4:6:8. Find the measure of ∠B.

Answer 1

Step-by-step explanation:

Given :-

In a pentagon ABCDE, side AB is parallel to side ED and ∠B:∠C:∠D is 4:6:8.

To find :-

Find the measure of ∠B ?

Solution :-

Given that

ABCDE is a Pentagon

AB || ED

We have AE is a transversal

∠ A + ∠ E = 180° ---------------(1)

Since the interior angles on the same side to the transversal are supplementary.

Given that :

∠B:∠C:∠D = 4:6:8.

Let ∠B = 4x°

Let ∠C = 6X°

Let ∠D = 8X°

We know that

The sum of all interior angles in a polygon of n sides is (n-2)×180°

We have , n = 5

Sum of all interior angles in the Pentagon

=> (5-2)×180°

=> 3×180°

=> 540°

Now,

∠A + ∠B + ∠C + ∠D + ∠E = 540°

=> ∠A + 4X° + 6X° + 8X° + ∠E = 540°

=> (∠A + ∠E ) + 18X° = 540°

=> 180° + 18X° = 540°

Since ,From (1)

=> 18X° = 540° - 180°

=> 18X° = 360°

=> X° = 360°/18

=> X° = 20°

Now, ∠B = 4X° = 4×20° = 80°

Answer :-

The measure of the ∠B in the given Pentagon is 80°

Used formulae:-

• The interior angles on the same side to the transversal are supplementary.
• The sum of all interior angles in a polygon of n sides is (n-2)×180°