Question

5.
In the figure given below, AB || CD and
PQ is the transversal, find Z CRS, LASP,
ZPSB and BSR.
C С
A
148°
Р
S
R.
Q
D
B

I NEED STEP BY STEP EXPLANATION ​

Answer 1

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GIVEN THAT,

AB || CD AND P IS TRANSVERSAL ,

ANGLE CRD = 148 DEGREES.

(i)

( since angle CRS and angle CRD ARE LINEAR PAIR , [SUM OF LINEAR PAIR = 180 DEGREES])

ANGLE CRD + ANGLE CRS = 180 DEGREES

148+ANGLE CRS =180 DEGREES

ANGLE CRS =180-148

=32 DEGREEES

(ii) ANGLE ASP = ANGLE CRS

ANGLE ASP = 32 DEGREES

( SINCE ANGLE ASP AND ANGLE CRS ARE CORRESPONDING ANGLES, NOTE: CORRESPONDING ANGLES ARE ALWAYS EQUAL IF THE LINES ARE PARALLEL)

(iii) ANGLE PSB = ANGLE CRD

ANGLE PSB = 148 DEGREES

( SINCE ANGLE PSB AND ANGLE CRD ARE ALTERNATE EXTERIOR, NOTE: ALTERNATE ANGLES ARE ALWAYS EQUAL IF THE LINES ARE PARALLEL)

(iv) ANGLE BSR = ANGLE ASP

( SINCE THEY ARE VERTICALLY OPPOSITE ANGLES, NOTE : VERTICALLY OPPOSITE ANGLES ARE ALWAYS EQUAL IF THE LINES ARE PARALLEL)

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