Question

in the diagram below A || B and C is a transformer. The sum of angles 1,2,3,4 and 5 is n x 46. Then n is _______​

Answer 1

PQRS is a parallelogram.

∠P = 60°

In a parallelogram, opposite angles are equal.

So, ∠P = ∠R

Measure of ∠R = 60°

We know that adjacent angles in parallelogram are supplementary, which means their sum is 180°.

Adjecent angles are ∠P and ∠S, ∠Q and ∠R.

\longrightarrow⟶ ∠P + ∠S = 180°

\longrightarrow⟶ ∠S + 60° = 180°

\longrightarrow⟶ ∠S = 180° - 60°

\longrightarrow⟶ ∠S = 120°

∠S is opposite to ∠Q,

\longrightarrow⟶ ∠S = ∠Q

\longrightarrow⟶ ∠Q = 120°

Therefore, angles of the parallelogram are :

∠P = 60°

∠Q = 120°

∠R = 60°

∠S = 120°

__________________

★ Verification:

Verifying by the angle sum property of a parallelogram.

Sum of all angles in a parallelogram is 360°.

\longrightarrow⟶ ∠P + ∠Q + ∠R + ∠S

\longrightarrow⟶ 60° + 120° + 60° + 120°

\longrightarrow⟶ 120° + 240°

\longrightarrow⟶ 360°

Hence verified.

Answer 2

Answer:

5

Step-by-step explanation:

angle 5 = 100° (vertically opposite angles)

1+2+3+4 =360° (complete angle )

1+2+3+4+5 =100° + 360° =460°

also sum of 1,2,3,4,5= 46n

so, 46n = 460°

so, n= 46°