Question

Given: AB ≅ BC and AE = 10 in, m∠FEC = 90° m∠ABC = 130°30' Find: m∠EBC, AC

Answer 1

Answer: uhhhh, what is the minute, just have this question

Explanation:

Answer 2

m∠EBC = 65.25°

AC=20 in.

Explanation:

We are given AB ≅ BC that means that side AB and side BC are equal also we know that angle opposite to equal sides are equal.

Hence, ∠BAE=∠BCE-------(1)

Also ∠AEB=∠CEB.

Now we are given that: ∠ABC = 130°30’ i.e. in degrees it could be given as:

60'=1°

30'=(1/2)°=0.5°

Hence ∠ABC = 130°30’=130+0.5=130.5°

Also we know that sum of all the angles in a triangle is equal to 180°.

Hence,

∠BAE+∠BCE+∠ABC=180°.

2∠BAE+130.5=180 (using equation (1))

2∠BAE=49.5

Dividing both sides by 2 we get;

∠BAE=24.75°

Now in triangle ΔBEC we have:

∠BEC=90° , ∠BCE=24.75°

SO,

∠BEC+∠BCE+∠EBC=180°.

Hence,
`90+24.75+ \angle EBC=180`

∠EBC=
`180-(90+24.75)`

∠EBC=65.25°

Now we are given AE = 10 in

Also ∠BEA= 90°.

And ∠BAE=24.75°; hence using trigonometric identity to find the measure of side BE.

`tan24.75=(BE)/(AE) = (BE)/(10)\\\\BE= 10 \ tan24.75 \ \ \ \ \ equation \ 2`

similarly in right angled triangle ΔBEC we have:

`tan24.75=(BE)/(EC)\\\\EC=(BE)/(tan24.75) \ \ \ \ \ \ \ \ \ equation \ 3`

Hence, using equation (2) in equation (3) we get:

`EC = (10 \ tan24.75)/(tan24.75) =10in`

Hence AC=AE+EC=10+10=20 in.

Hence side AC=20 in.