Question

Calculate the value of x in the figure:​

Answer 1

90⁰+40⁰+ < ABC = 180⁰

Angle ABC = 50⁰

50⁰+100⁰+x = 180⁰

x = 30⁰

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Answer 2

$\LARGE\sf {\underline{\underline\green{Required \:  Answer:-}}}$

∆ABC, We have:

$\sf{∠BAC + ∠ABC + ∠BCA = 180⁰(Sum \: of \: angles \: of \: a \: triangle)}$

$\sf\implies{40⁰ + ∠ABC = 90⁰ = 180⁰}$

$\sf\implies{∠ABC + 130⁰ = 180⁰}$

$\sf\implies{∠ABC = (180⁰-130⁰) = 50⁰}$

In ∆BDE, We have:

$\sf{∠EBD + ∠BDE + ∠DEB = 180⁰(Sum \: of \: angles \: of \: a \: triangle)}$

$\sf{∠ABC + ∠BDE + ∠DEB = 180⁰}$

$\sf \implies{50⁰ + x⁰ + 100⁰ = 180⁰}$

$\sf \implies{x⁰ + 150⁰ = 180⁰</p><p>}$

$\sf\implies{x⁰ = (180⁰-150⁰)=30⁰}$

Hence, x = 30⁰

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