Answer:
x = 40 degrees
Step-by-step explanation:
There are heaps of different ways to do this, but this is how i got the answer. I think you'll find it a lot easier if you annotate the diagram as you go; at least that's what i did :)
So to figure out x, we need to find the two other angles in the big triangle, angle ADC and DCB. Since we know that all 3 angles in ANY triangle ALWAYS add up to 180 degrees, we'll be able to solve for x if we know these 2 angles.
To find angle ADC:
- we were told what ADB is and what BDC is. if you add these two values, you'll get ADC.
- so, 20 + 40 = 60 degrees.
<u>So, now we know that ADC = 60 degrees. </u>
To find angle DCB:
- we know that triangle DCB is an isoceles (because of the tow little lines on lines BD and CD)
- this means that angles DBC and DCB are exactly the same
- now, we know that all the angles in this little isoceles add up to 180 degrees as well.
- we know that angle BDC is 20 degrees.
- If we do 180 - 20, we get 160 degrees.
- now we know that the sum of angles DBC and DCB are 160 degrees.
- since both angles are the same, we can just divide it by 2 and we get that DCB is 80 degrees.
<u>So, now we know that the second angle DCB in the big triangle is 80 degrees. </u>
To find x:
All we have to do is 180 - ADC - DCB
= 180 - 60 - 80
= 40 degrees
<u>So, x=40 degrees</u>
Sorry if that was really long and confusing. Hope it helped a little :)
