Question

in ∆ ABC measure of angle A= X° , measure of angle b =3x°, measure of angle C = y° and 3Y - 5x is equal to 30. find the measure of all angles of ∆ ABC hence prove that ∆ ABC is a right angled triangle​

Answer 1

Answer:

we know that sum of all the angles of a triangle is 180

so

A + B+ C = 180

X + 3X + Y = 180

4x + y = 180-------------1 eq

now we have given

3y - 5x = 30

so y = 30 +5x/3 ---------------------2 eq

substituting value of y in eq 1

4x + 30 + 5x/ 3 = 180

taking lcm to get

12x +30 + 5x / 3 = 180

12x+ 30 + 5x = 180 * 3

17x + 30 = 540

17x = 510

x = 30

substituting value of x in equation 2

3y - 5x = 30

3y - 150 = 30

y = 180/3

y = 60

so  a = 30  c = 60 and B = 3*30 = 90

hence it is a right angled triangle

Step-by-step explanation:

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