Question

NEED HELP ASAP Find the measure of angle x in the figure below:

45
55
45°
80°
55°
100°​

Answer 1

80°

Explanation:

We have redrawn the figure with nomenclature.

Given,

∠C = 45°

∠D = 55°

We have to find the value of x.

Solution,

In ΔCDE

`\angle C = 45\°\\\\ \angle D = 55\°`

Now according to angle sum property;

Sum of all the angles of a triangle is equal to 180°.

framing in equation form, we get;

`\angle C+\angle D+\angle E =180\°`

On substituting the given values, we get;

`45+55+y=180\°\\\\100+y=180\°\\\\y=180\°-100\°\\\\y =80\°`

Now In Δ AEB and Δ CED

`m \angle AEB =m\angle CED` ⇒ (Vertically opposite angles.)

Now
`m\angle CED = y\°= 80\°`

So
`m\angle AEB =x\°= 80\°`

Hence
`x =80\°`.