Question

find x and y

explain properly

Answer 1

Answer:

x = 30

y = 50

Step-by-step explanation:

x = 30 = corresponding angles

y = 50 = alternate angles

Answer 2

To find:-

The values of x and y.

Note:-

Firstly label the figure. (refer to the attachment provided)

Solution:-

In ∆ABD

$\sf{\angle ADB = 50^\circ}$

$\sf{\angle BAD = 30^\circ}$

According to angle sum property of a triangle,

Sum of all the angles of a triangle is always 180°

Therefore,

$\sf{\angle ADB + \angle BAD + \angle ABD = 180^\circ}$

= $\sf{50^\circ + 30^\circ + \angle ABD = 180^\circ}$

= $\sf{80^\circ + \angle ABD = 180^\circ}$

= $\sf{\angle ABD = 180^\circ - 80^\circ}$

= $\sf{\angle ABD = 100^\circ}$

Now,

$\sf{\angle ABD + \angle CBD = 180^\circ\:\:\longrightarrow[Linear\:Pair]}$

= $\sf{100^\circ + x = 180^\circ}$

= $\sf{x = 180^\circ-100^\circ}$

= $\sf{ x = 80^\circ}$

Now,

In ∆CBD

$\sf{\angle CBD = 80^\circ}$

$\sf{\angle DCB = 45^\circ}$

According to angle-sum property of a triangle,

$\sf{\angle CBD + \angle DCB + \angle CDB = 180^\circ}$

= $\sf{80^\circ + 45^\circ + \angle CDB = 180^\circ}$

= $\sf{125^\circ + \angle CDB = 180^\circ}$

= $\sf{\angle CDB = 180^\circ - 125^\circ}$

= $\sf{\angle CDB = 55^\circ}$

Now,

$\sf{\angle EDC + \angle CDB + \angle ADB = 180^\circ \:\:\longrightarrow[Linear\:Pair]}$

= $\sf{y + 55^\circ + 50^\circ = 180^\circ}$

= $\sf{y + 105^\circ = 180^\circ}$

= $\sf{y = 180^\circ - 105^\circ}$

= $\sf{y = 75^\circ}$

Therefore,

$\sf{x = 80^\circ}$

$\sf{y = 75^\circ}$

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