Question

In the given figure, ABCD is a square. A line BM intersects CD at M and diagonal AC at O such that LAOB = 80 degrees. Find the value of x.

Answer 1

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!}}}$

Here is your answer in the attachment

$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope\:it\:helps\: you}}}}}}}}}}}}}}}$

Answer 2

Given:

Angle AOB=80°

ABCD is a square

To find:

The value of x

Solution:

We can find the angle by following the given steps-

We know that the measure of the angle x can be determined by using the exterior angle property of triangles.

As per the property, angle DMO is equal to the sum of the angle MOC and MCO.

In square ABCD, each angle is equal to 90°

Diagonal AC bisects the angle C and so, the angle MCO= 1/2× angle C

=1/2×90

=45°

BM and AC are transversals between two parallel lines AB and CD.

So, angle AOB= angle MOC (Vertically opposite angles)

Now, the angle x= angle MOC +angle MCO

x=80+45

x=125°

Therefore, the value of x is 125°.