Question

class 7 sub maths plz say full answer with full methods​

Answer 1

Answer:

55°

Step-by-step explanation:

Given :-

Isosceles triangle in which LM = LN

∠KOM = 70°

To find :-

Value of 'z'

Solution :-

At point L (MLO line)

Applying linear pair

∠MLK + ∠KLO = 180°

∠MLK + 70° = 180°

∠MLK = 180° - 70°

∠MLK = 110°

We know that in an isosceles triangle, angles opposite to equal sides are equal

∴ ∠LMN = LNM = z

∠LMN + ∠LNM = ∠MLK (Exterior angle is the sum of opposite interior angles)

z + z = 110°

2z = 110°

z = 110°/2

z = 55°

(Alternate method)

∠KLO = ∠MLN = 70° (Vertically opposite angle)

∠LMN = ∠LNM = z (Angles opposite to equal side)

We know that sum of interior angles of a triangle is 180°

∴ ∠MLN + ∠LMN + ∠LNM = 180°

   70° + z + z = 180°

   2z = 110°

   z = 110°/2

   z = 55°