Question

What can be the angle measurement of x ???

Answer 1

ABCD is a rectangle. So, AO = OC & BO = OD
Also, AC = BD.
AO + OC = AC & BO + OD = BD
=>AO + OC = BO + OD
=>2AO = 2BO
=>AO = BO
=>Angle OAB = Angle OBA (Angles opposite to equal sides are equal)
Angle OBA = 21 Degrees
Also, Angle ABC = 90 Degrees (Angle in a rectangle is 90 degrees)
=>Angle OBA + Angle OBC = 90 Degrees
=>x + 21 = 90
=>x = 90 - 21 = 69 degrees

Hope this helps you... Please mark it as brainliest!!!

Answer 2

Hey there,
According to the diagram,

AC is intersecting from one vertex to another so,

Ang. OBA = Ang. OAB = 21°

In ∆ OAB,

=> 21° + 21° + Ang. AOB = 180°
=> Ang. AOB = 180° - 42°
=> Ang. AOB = 138°

AC is a straight line so it is 180°

Then,

Ang. COB = 180° - 138° = 42°

As AC is intersecting two vertexes,

So In ∆ COB,

=> x + x + 42° = 180°
=> 2x = 180° - 42° = 138°
=> x = 138° / 2 = 69 °

Then x = 69°

Answer. x is 69°

Hope it helps !!!

Regards,
AritraK • Expert •