Question

In triangleABC, angleA - angleB =15°, AngleB - angleC= 30°,find AngleA, angleB and angleC

Answer 1

angle A - angleB=15
angleA = 15 + angleB

angleB - angleC = 30
angleC = -30 + angleB


Now,
the sum of all interal angles of triangle is 180

therefore angleA + angleB + angleC = 180
therefore (angleB+15) + angleB + (angleB-30) = 180
therefore. 15 - 30 + angleB + angleB + angleB = 180
therefore. -15 + 3 ×angleB = 180
therefore. 3 × angleB = 180 + 15
therefore. 3 × angleB = 195
therefore. angle B = 195 ÷ 3
therefore. angleB = 65



Now,
angleB = 65
so,
angleA = 15 + angleB
= angleA = 15 + 65
= angleA = 80


angleC = -30 + angleB
= angleC = -30 + 65
= angleC = 35




therefore. angleA = 80, angleB = 65 & angleC = 35