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Class 10 > Learn Mathematics > The exterior angles obtained on producing the base...
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The exterior angles obtained on producing the base of a triangle both ways are 100° and 120°. Find all the angles.

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As we know the triangle, parallelogram standing on the same side and between same parallel lines then ar(Triangle) = 1/2.ar(parallelogram) and ar(parallagoram) = 2, ar(triangle) = 2 (15) cm.sq ar of Parallelogram ABPD = 30cm.sq
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1) Draw PQRS Square, Mark Point T on PS which is bisecting PS, Mark U on QR which is bisecting QR. 2) Join SQ where SQ intersects TU at 'O' 3) Now you can find two triangles STO, SPQ so prove both the triangles are similar( ang STO = ang SPQ corresponding, ang TSO = ang PSQ common angles ) 4) as we know...
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1) Draw PQRS Square, Mark Point T on PS which is bisecting PS, Mark U on QR which is bisecting QR. 2) Join SQ where SQ intersects TU at 'O' 3) Now you can find two triangles STO, SPQ so prove both the triangles are similar( ang STO = ang SPQ corresponding, ang TSO = ang PSQ common angles ) 4) as we know if two triangles are similar then their corresponding sides are in proportion so ST/SP = TO/PQ 4/8 = TO/8 cancelling both same denominators will get the length of TO is 4cm 5) now ar(STO ) = 1/2 *b*h = 1/2(4*4) = 1/2(16) = 8sq.cm read less
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Let A, B and C be the vertices of the triangle with B and C as the base vertices. If the external angle at C is 100 degrees then the angle C is 80 degrees (because sum of adjacent angles on a straight line is 180 degrees). Similarly if the external angle at B is 120 degrees then the angle B is 60 degrees....
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Let A, B and C be the vertices of the triangle with B and C as the base vertices. If the external angle at C is 100 degrees then the angle C is 80 degrees (because sum of adjacent angles on a straight line is 180 degrees). Similarly if the external angle at B is 120 degrees then the angle B is 60 degrees. So the angle A is 40 degrees. i.e. 180 - (80 + 60).

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Let the apex angle be A , moving clock wise the other angle be B and the let the third angle be C A+C=100 A+B=120 A+B+C=180 There are three variables and 3 equations Therefore B=80 C=60 A=40
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So the interior angles are 80 and 60 respectively and the third angle is (180-80-60) = 40 Ans
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