Please slove question 37 Q 37 If one angle of a triangle is 110 , then the angle between - Maths - Triangles

Question

Please slove question 37
Q 37 If one angle of a triangle is 110 ° , then the angle
between the bisectors of exterior angles of the two angles is:
(A) 55 °
(B) 65 °
(C) 45 °
(D) 35 °

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

Here BP and CP are the angle bisectors of exterior angles ∠CBD and ∠BCESo,∠CBP=∠CBD2 and ∠BCP=∠BCE2∠A=110°       GivenIn △ABC,∠A+∠B+∠C=180°  
1   Angle Sum Property∠CBD=∠A+∠C    
 2∠BCE=∠A+∠B   
 3Adding 2 and 3 , we get∠CBD + ∠BCE= ∠A+∠A +∠B+∠C∠CBD + ∠BCE= 110°+180°                         Using 1 ∠CBD + ∠BCE= 290°Now,In ∆BCP∠CBP+∠BCP+∠BPC=180°         Angle Sum Property∠CBD2+∠BCE2+∠BPC=180°∠CBD + ∠BCE2+∠BPC=180°290°2+∠BPC=180°145°+∠BPC=180°∠BPC=35°     ANS
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Please slove question 37 Q.37. If one angle of a triangle is 110 ° , then the angle between the bisectors of exterior angles of the two angles is: (A) 55 ° (B) 65 ° (C) 45 ° (D) 35 °

Please slove question 37
Q.37. If one angle of a triangle is 110 $°$ , then the angle between the bisectors of exterior angles of the two angles is:
(A) 55 $°$
(B) 65 $°$
(C) 45 $°$
(D) 35 $°$