Question

Find the values of x and y​

Answer 1

Angle D of Triangle BCD = 180 - 85 = 95

So, $x$ = 180 - (95 + 40)

         = 45

$y$ = 180 - (85 + 50)

  = 45

Answer 2

Answer:

• Value of x is 45 and value of y is also 45.

Step-by-step explanation:

To Find:

• Value of x and y

Solution:

• Value of y

In triangle ACD the sum of all angles is $180^\circ$ (Angle sum property of triangle).

$\therefore 50^\circ+85^\circ+y^\circ=180^\circ\\\implies y^\circ=180^\circ-50^\circ-85^\circ\\\implies y^\circ=180^\circ-135^\circ\\\implies y^\circ= 45^\circ$

Hence, the value of y is $45^\circ$.

• Value of x

In triangle BCD $\angle CDB=180^\circ-\angle CDA$ (Linear pair).

$\therefore \angle CDB=180^\circ-85^\circ\\\implies \angle CDB = 95^\circ$

Since $\angle CDB=95^\circ$, sum of all angles of triangle is $180^\circ$ (Angle sum property of triangle).

$\therefore 40^\circ+95^\circ+x^\circ = 180^\circ\\\implies x^\circ=180^\circ-40^\circ-95^\circ\\\implies x^\circ=180^\circ-135^\circ\\\implies x^\circ=45^\circ$

Therefore, value of x is 45 and value of y is also 45.

Extra Information:

• Angle sum property of triangle - Sum of all angles of a triangle is $180^\circ$.
• Exterior angle property of triangle - Exterior angle of triangle is equal to the sum of two interior opposite angles.
• The sum of any two sides of a triangle is greater than the third side.
• Pythagoras Theorem - In right angle triangle the hypotenuse is equal to the sum other two angles.