Question

In a regular pentagon ABCDE, draw
diagonal BE and then find the measure of :
(1) ZBAE (ii) ZABE (ii) ZBED​

Answer 1

Given:

• A Pentagon ABCDE
• a diagonal BE

To Find:

measure of :

↪∠BAE

↪∠ABE

↪∠BED

Solution:

1) Since number of sides in the Pentagon = 5

$⟹$each exterior angle$= \frac{360}{5} = 72°$

$⟹$∠BAE = 180° - 72°

$⟹$${\small\underline{\sf{\red{∠BAE = 108°}}}}$

2) in ∆ABE, AB = AE

$∴$∠ABE = ∠AEB

But ∠BAE + ∠ABE + ∠AEB = 180°

$∴$108° + 2∠ABE = 180° - 108° = 72°

$⟹$ ∠ABE = 72°/2

$⟹$${\small\underline{\sf{\red{∠ABE\:=\:36°}}}}$

3)Since,∠AED = 180° [∵ each interior angle = 180°]

$⟹$∠AEB = 36°

$⟹$∠BED = 108° - 36°

$⟹$${\small\underline{\sf{\red{∠BED\:=\:72°}}}}$

Hence:

$➙$∠BAE = 108°

$➙$∠ABE = 36°

$➙$∠BED = 72°

Answer 2

$\huge \bold{answer}$

ABCDE is a regular pentagon

sum of interior angles of polygon= ( N-2) × 180

here,

N= 5

therefore

(5-2)× 180

= 3× 180

= 540°

since all the 5 angles of a regular pentagon are equal measure , each angle is

540/5 = 108°

so angle BAE= 108°

In ∆ ABE ,

AB=AE

angle BAE+ angle AEB+ angle ABE =180°

108+ 2( ABE)= 180°

therefore,

angle ABE= 36°

Now,

Angle BED= 180°-108°=72.

hope it is useful for you