The exterior angles obtained on producing the base of a triangle both ways are 70° and 130°. Find all the interior angles.
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Step-by-step explanation:
please,see the given figure...
Now, in the given figure base BC produced to D and E. then,
<ABE=70° and <ACD=130°.
<ABE+ <ABC =180°. (by linear pair)
70° + <ABC =180°
•°•<ABC =180°-70°=110°.
Again, <ACD+ <ACB=180°. (by linear pair).
130°+ <ACB=180°
•°•<ACB=180°-130°=50°.
Since,in ∆ABC we have:-
<ABC+ <ACB+ <BAC=180°. (sum of <s of triangle)
110°+50°+ <BAC =180°
•°•<BAC =180°-160°
=20°....
Hence,all interior angles of triangle are
<ABC=110°,<ACB=50° and <BAC=20° ...
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