Question

please my questions answer

Answer 1

Construction: Draw a ray RU║PQ

Take ∠QRU as ∠1

and ∠URS as ∠2

∵PQ║ST

∴RU║ST( lines ║ to the same line are ║to each other)

Now, x+∠1 =180°(Co-interior angles)

SImilarly, y+∠2=180°

So, x+y+∠1+∠2=360°

⇒x+y+100°=360°(∠1+∠2=100°)

⇒x+y=260°

Also, difference between measures of x and y is 58°

So, two cases are possible.

CASE - 1

y > x

SO, y-x=58°

∵x+y=260°

⇒x=260-y

∴y-(260-y)=58°

⇒y-260+y=58°

⇒2y=260°+58°

⇒y=318°/2

⇒y=159°

so, x=260-y

⇒x=101°

CASE - 2

x > y

x-y=58°

Following the procedure given in CASE 1 we will get x=159° and y=101°

∴x can be 159° or 101°

If x=159°

then, y=101°, and

If x=101°

then, y=159°