Question

In the given figure, find x

Answer 1

Answer:

x = 109°

Step-by-step explanation:

Given

$i) \bold{ \angle \: C = 30 ^{ \circ} }$

$ii)\bold{ \angle \: A = 34 ^{ \circ} }$

$iii) \bold{ \angle \: D= 45 ^{ \circ} }$

To find :

$i) \: x$

Procedure :

It's clearly understood just by looking at the figure that we have two triangles

i) ∆ ABC

ii) ∆ EBD

Since , in a triangle sum of all sides are 180°. Then ,

(In ∆ ABC)

$\sf \: 34 + 30 + \angle \: B \: = 180 {}^{ \circ}$

$\sf \implies \: 64 + \angle \: b = 180$

$\sf \implies \: \angle \: b = 116$

---------------------------------

Now at B ,

$\sf \angle3 + \angle4 = 180 {}^{ \circ} (linear \: pair)$

$\sf \implies \: 116 + \angle4 = {180}^{ \circ}$

$\sf \implies \angle4 = {64}^{ \circ}$

---------------------------------

Now,

In ∆EBD

$\sf \implies \: 64 + 45 + \angle \: E = 180$

$\implies \angle \: E= 71$

---------------------------------

$\sf \implies \: \angle \: 1 + \angle2 = 180 (linear pair)$

$\sf \implies \: x+71= 180$

$\sf \implies \: x= 109$