Q. 15.0( 2 Votes )

# <span lang="EN-US

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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