Question

please what is the value of x and y ​

Answer 1

Answer:

x= 33°

y= 82°

Step-by-step explanation:

For x:-

Sum of all interior angles of a triangle= 180°

40°+107°+x= 180°

x= 180°-147°

x= 33°

For y:-

x+65°+y= 180°

33°+65°+y= 180°

y= 180°-98°

y= 82°

Answer 2

$\large\underline{\sf{Solution-}}$

In triangle ADC

∠DAC = 40°

• ∠ADC = 107°

• ∠ACD = x°

Now,

We know that, Sum of all interior angles of a triangle is supplementary.

Thus,

∠ADC + ∠DAC + ∠ACD = 180°

⇛ 40° + 107° + x° = 280°

⇛ 147° + x = 180°

⇛ x = 33°

$\\ \rm\implies \:\boxed{\tt{ \angle \: ACD \: = \: 33 \degree \: }}$

Now, ACE is a line.

So,

∠ACD + ∠DCB + ∠BCE = 180°

⇛ x + 65° + y = 180°

⇛ 33° + 65° + y = 180°

⇛ 98° + y = 180°

⇛ y = 180° - 98°

⇛ y = 82°

$\\ \rm\implies \:\boxed{\tt{ y \: = \: 82 \degree \: }}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

More to Know :-

1. Exterior angle of a triangle is equals to sum of interior opposite angles.

2. Angle opposite to longest side is always greater.

3. Side opposite to greatest angle is always longest.

4. Angle opposite to equal sides are always equal.

5. Side opposite to equal angles are equal.