Question

The exterior angles obtained on producing the base of a triangle both ways are 70° and 130°. Find all the interior angles.

Answer 1

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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