Question

If Figure, if $y>60$ and $AB=BC$, select the correct statement(s).
I. $a+y=180$
II. $y>z$
III. $a=y+z$

• A. I only
• B. II only
• C. III only
• D. I and II
• E. II and III

Answer 1

Answer: (E)

II and III

In given figure, $ABC$ is a triangle

then $\angle x+\angle y+\angle z=180$

The line $AC$ extended above

Then $\angle a+\angle z=180$

(I) $\angle a+\angle y=180$ is wrong because $\angle x+\angle y+\angle z=180$

(II) $\angle y>\angle z$ is correct because $\angle a+\angle z=180$ and $\angle x+\angle y+\angle z=180$

So $\angle y>\angle z$

(III) $\angle a=\angle y+\angle z$ is correct because $\angle a+\angle z=180$ and $\angle x+\angle y+\angle z=180$

So $\angle a=\angle y+\angle z$

Then (II) and (III) statements are correct