document.write( "Question 1062119: in a quadrilateral STUV the bisectors of angle U and angle V meet at a point O. if angle T=80 and angle S=60. find angle UOV
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in a quadrilateral STUV the bisectors of angle U and angle V meet at a point O. if angle T=80 and angle S=60. find angle UOV
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OU is the bisector of ∠U, and OV is the bisector of ∠V
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document.write( "Note that OV and OU form 2 sides of the triangle, OVU \r
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document.write( "Let ∠SVO be x
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document.write( "Then ∠OVU also = x\r
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document.write( "Likewise, let ∠TUO be y
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document.write( "Then ∠OUV also = y\r
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document.write( "Since the interior angles of a quadrilateral sum to , we get:
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document.write( "2x + 2y + 60 + 80 = 360
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document.write( "2x + 2y + 140 = 360
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document.write( "2x + 2y = 220____2(x + y) = 2(110)_____x + y = 110
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document.write( "Since x and y are the 2 base angles of triangle, OVU, it follows that ∠UOV = 180 - (x + y), or 180 - 110 =  \n" );
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