Question

b) In the adjoining figure, show that x+y+z=180° ​

Answer 1

Answer:

Proved

Step-by-step explanation:

Linear Pair Theorem:

• Let any number of lines divide equally or unequally the angles on a straight line so formed. The angles' sum on that line equals 180°.

Here we see two lines divide a straight line into three parts: at parts of <a,<b,<z.Their sum must equal 180°

• It follows <a+<b+<z = 180° ...(i)

Two lines are parallel as shown.

By alternate angle theorem

• Theorem states in two || lines, the angles on the transversal which lie alternative are equal. Just remember they form a "Z".

Therefore here

• <x = <a
• <y = <b

Putting these value in eqn (i)

• <x+<y+<z = 180°

...Proved