Question

step by step solution please​

Answer 1

Step-by-step explanation:

Exterior angle = 120 degree.

one of the opposite interior angle = 40 degree.

second opposite interior angle = 120 -40 = 80 degree ( exterior angle of a triangle is the sum of the two opposite interior angles ).

Third angle = 40 + 80 + x = 180

= 120 + x = 180

= x = 180 - 120

= x = 60 degree( angle sum property of triangle ).

Therefore, Angles of the triangle are 40 degree, 80 degree and 60 degree.

Answer 2

Given :

⠀⠀⠀⌬ Exterior angle of a triangle = 120°

⠀⌬ One of its interior opposite angles = 40°

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To find :

• The other two angles (i.e., ∠BAC and ∠ACB) of the triangle.

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Solution :

In ∆ABC , BC is produced to D.

Let ‎ -

• ∠ACD (exterior angle) = 120° and
• ∠ ABC (one interior angle) = 40°

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We know ,

$\sf\color{olive}{Exterior~angle~=~Sum~of~interior~opposite~angles}$

$\sf\longrightarrow\:∠ACD~=~∠BAC+∠ABC$

Substituting the values

$\sf\longrightarrow\:120°~=~∠BAC+40°$

$\sf\longrightarrow\:120°-40°~=~∠BAC$

$\sf\longrightarrow\:80°~=~∠BAC$

$\small{\underline{\boxed{\mathrm{\longrightarrow\:∠BAC=80°}}}}$ $\sf\color{teal}{⋆}$

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Now using the angle sum property of the triangle -

$\bf\dag$ $\sf\color{olive}{Sum~of~three~angles~=~180°}$

$\sf\longrightarrow\:∠ABC+∠BAC+∠ACB=180°$

Substituting the values

$\sf\longrightarrow\:40°+80°+∠ACB=180°$

$\sf\longrightarrow\:120°+∠ACB=180°$

$\sf\longrightarrow\:∠ACB=180°-120°$

$\small{\underline{\boxed{\mathrm{\longrightarrow\:∠ACB=60°}}}}$ $\sf\color{teal}{⋆}$

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$\bf\therefore\:∠BAC~=~80°~and~∠ACB~=~60°$

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I have provided the figure of the triangle in the attachment , just refer to it while viewing the solution !