Question

Find the value of x from the following figure​

Answer 1

Answer:

x=110°

Step-by-step explanation:

Const:- Produce AE to D such that D is a point on BC.

$\small{In \: } \triangle{ \: ABD, we \: have }$∠ABD+∠BDA+∠BAD=180°(angle sum property)

$\small\implies{∠45°+∠BDA+35°=180°}$

$\small\implies{80°+∠BDA=180°}$

$\small\implies{∠BDA=180°-80°}$

$\small\implies{∠BDA=100°}$

Since, ∠BDA + ∠CDE = 180°(Linear pair)

$\small\implies{∠CDE=180°-∠BDA}$

$\small\implies{∠CDE=180°-100°}$

$\small\implies{∠CDE=80°}$

$\small{In \: } \triangle{ \: EDC, we \: have }$

∠CDE+∠DCE=∠AEC (Exterior angle property)

$\small\implies{80°+30°=x}$

$\small\implies{x=110°}$

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