Question

19. In the given figure, L || m. If PQU, QRV and PRS are straight lines, then find the measures of a, b, c, d and e.​

Answer 1

Thanku

A=101

B=50

C=29

D=151

E=29

Answer 2

The measure of angles are-

∠a = 101°

∠b = 50°

∠c = 29°

∠d = 151°

∠e = 29°

GIVEN

l || m

PQU, QRV, and PRS are straight lines.

TO FIND

The measure of angles a, b, c, d, and e.

SOLUTION

We can simply solve the above problem as follows;

We know that,

Angle of a straight line = 180°

So,

∠UQR + ∠PQR = 180°

79° + ∠PQR = 180°

∠PQR = 180- 79 = 101°

In ΔPQR

∠PQR + ∠QPR + ∠QRP = 180°

(Sum of interior angles in a triangle is 180°)

Putting the values in the above

101 + 50 + ∠QRP = 180

151 + ∠QRP = 180

∠QRP = 180-151 = 29°

∠QRP = ∠c = 29°

We know that when a straight line is intersected by a transverse line, vertically opposite angles are equal.

QRP is a straight line , intersected by a transverse line PRS .

∠c = ∠e = 29° (Vertically opposite angle)

We know that,

∠UQR = ∠TRV (corresponding angles of a transverse line)

79° = ∠b + ∠e

79° = ∠b + 29°

∠b = 79-29

∠b = 50°

We know that,

∠a + ∠b + ∠e = 180° (sum of angles of a straight line)

∠a + 50 + 29 = 180

∠a = 180-79

∠a = 101°

We know that,

∠c + ∠d = 180° (sum of angles of a straight line)

∠d = 180-29 = 151°

Hence, The measure of angles are- a = 101° ∠b = 50°∠c = 29°∠d = 151° ∠e = 29°

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