Question

In a triangle if measure of one of the Exterior angle is 140 degree and other two Exterior angles are equal. Find the measure of the equal Exterior angles.
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Answer 1

Answer:

This might help you

Step-by-step explanation:

Let the other two sides be x and y

x+y= 140°( Exterior angle property )

x=y ( Given)

x+x=140°[x=y]

2x=140°

x= 70°

Answer 2

Correction in the Question :

• It should be other two interior angles instead of exterior angles.

AnswEr :

We're given that the exterior angle of the triangle measure 140° and other 2 interior angles are equal.

Firstly we'll calculate the value of the adjacent interior angle with the given exterior angle, that is, 140°.

⋆ Diagram is given below :

$\\ \setlength{\unitlength}{2.2mm} \thicklines\begin{picture}(30,20)\put(10,9){\large {\sf{A}}}\put(-5,-5){\large{ \sf{B}}}\put(16,-5){\large{ \sf{C}}}\put(-3,-3){\line(1,1){12}}\put(-3,-3){\line(1,0){27}}\put(17,-3){\line(-2,3){8}}\put(16.9,-2){\large{ \sf{ {140}^{ \circ} }}}\end{picture}$

Also, we know that,

Any exterior angle with it's interior angle would always measures as 180°.

As,

$\\ : \implies \sf \: \: Interior \: angle + exterior \: angle = {180}^{ \circ}$

So,

$\\ \bullet \: {\underline {\sf{Interior \: angle :}}}$

$: \implies\sf \: {180}^{ \circ} - exterior \: angle \\ \\ \\ : \implies\sf \: {180}^{ \circ} - {140}^{ \circ} \\ \\ \\ : \implies\sf \: { \blue{40}^{ \circ} }$

Also,

$\\ \bigstar \: {\underline{\sf \: Sum \: of \: the \: interior \: angles : }}\\ \\ \\:\implies \sf \: {180}^{ \circ} - {40}^{ \circ} \\ \\ \\:\implies \sf \:{ \red{140}^{ \circ}}$

Now, let's calculate the value of other 2 interior angles,

$\bigstar \: {\underline{\sf \: Value \: of \: other \: 2 \: angles : }} \\ \\ \\ :\implies \sf \:\dfrac{ {140}^{ \circ} }{2} \\ \\ \\ :\implies \sf \:{ \purple{70}^{ \circ}} \: \: \: \: \: \: \: \: \: \: \bigg (As \: both \: angles \: are \: equal \bigg)$

Therefore, the 3 interior angles of the triangle are :

• 40°
• 70°
• 70°