Q. 15.0( 2 Votes )

Some isosceles triangles are drawn below. In each, one angle is given. Find the other angles.


Answer :

In first figure,

As seen it seems AB = BC (since it is a isosceles triangle).


Also, if 2 sides of a triangle are equal, the angles opposite equal sides are also equal.


BAC(A) = BCA(C) = 30°


In a triangle,


Sum of all angles of a triangle is 180°


Hence, in Δ ABC,


A + B + C = 180°


30 + B + 30 = 180°


B + 60 = 180°


B = 180-60


= 120°


In second figure,


As seen it seems DE = DF (since it is a isosceles triangle).


Also, if 2 sides of a triangle are equal, the angles opposite equal sides are also equal.


DEF(E) = DFE(F) = y° …(eq)1


In a triangle,


Sum of all angles of a triangle is 180°


Hence, in Δ DEF,


D + E + F = 180°


40 + y + y = 180°


40 + 2y = 180


2y = 180-40


= 140°



Hence, E = F = 70° (from eq1)


In 3rd figure,


As seen it seems PQ = PR (since it is a isosceles triangle).


Also, if 2 sides of a triangle are equal, the angles opposite equal sides are also equal.


PQR(Q) = PRQ(R) = y° …(eq)1


In a triangle,


Sum of all angles of a triangle is 180°


Hence, in Δ PQR,


P + Q + R = 180°


20 + y + y = 180°


20 + 2y = 180


2y = 180-20


= 160°



Hence, Q = R = 80° (from eq1)


In 4th figure,


As seen it seems XY = XZ (since it is a isosceles triangle).


Also, if 2 sides of a triangle are equal, the angles opposite equal sides are also equal.


XYZ(Y) = XZY(Z) = m° …(eq)1


In a triangle,


Sum of all angles of a triangle is 180°


Hence, in Δ XYZ,


X + Y + Z = 180°


100 + m + m = 180°


100 + 2m = 180


2m = 180-100


= 80



Hence, Y = Z = 40° (from eq1)


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