Question

Find the unknown sizes of angles​ (Urgently needed please help to solve)

Answer 1

Answer:

x=70, y=40, z=70

Step-by-step explanation:

So whenever you have a straight line, the angle is going to be 180 degrees, and whenever you have multiple angles that make up one angle, the sum of the multiples angles is going to be the angle of the one angle.

So let's look at x. The 180 degree angle consists of 110 degrees and x, the sum of these two should add up to 180 degrees, you can set up an algebraic equation to solve for x, but you can also do some simple mental math to see that x=70, so that 110+70=180. You do the same thing for the other angles

For y, you simply need to know 140+y = 180 so y=40

For z there is two methods, you can use the fact that opposite angles are congruent, or you can use the fact that the sum of the interior angles of a triangle is 180 degrees. This means that x+y+z=180 and since we know that x=70 and y=40 then 70+40=z so 110+z=180 so z=70, which is also the same as the opposite angle, you could use either method although knowing that opposite angles are congruent is much more easier. It's called the vertical angles theorem.