Question

In Figure 3, ABCD is a parallelogram. Find the measure of x and y.​

Answer 1

Answer:

x= 20°

y= 50°

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :-

ABCD is a Parallelogram,

<A = (3x+15)°

<B = (2y+5)°

<C = (2x+35)°

To find :-

Find the measures of x and y ?

Solution :-

Given that

ABCD is a Parallelogram,

<A = (3x+15)°

<B = (2y+5)°

<C = (2x+35)°

We know that

Opposite angles are equal in a Parallelogram.

=> <A = <C and <B = <D

=> 3x°+15° = 2x°+35°

=> 3x° - 2x° = 35°-15°

=> x° = 20°

Therefore, x = 20°

and

We know that

Adjacent angles are supplementary in a Parallelogram

=> <A+<B = 180°

=> 3x°+15° + 2y°+5° = 180°

=> 3(20°)+15° + 2y°+5° = 180°

=> 60°+15° +2y°+5° = 180°

=> 75° +2y°+5° = 180°

=> 80° +2y° = 180°

=> 2y° = 180°-80°

=> 2y° = 100°

=> y° = 100°/2

=> y° = 50°

Therefore, y = 50°

Answer:-

The measures of x and y are 20° and 50° respectively.

Check :-

If x = 20° then <A = 3(20°)+15° = 75°

and <C = 2(20)°+35° = 75°

<A = <C

and

If y = 50° then <B = 2(50°)+5° = 105°

So, <A + <C = 75°+105° = 180°

They are supplementary.

Verified the given relations in the given problem.

Used formulae:-

→ Opposite angles are equal in a Parallelogram.

→ Adjacent angles are supplementary in a Parallelogram