Question

1. In the given figure, if PQ || RS, then find the measure of angle m
With All The Formulae Step By Step
please​

Answer 1

$\bold { \red{EXPLANATION : }}$

GIVEN:

$\angle QPS = 56 \degree$

$\angle TRS = 14 \degree$

TO FIND:

$\angle RTS =?$

i.e angle m

SOLUTION:

$\angle QPS= \angle PSR$

------( Line PQ || Line RS, where PS is transversal)

$\therefore \angle PSR = 56 \degree$

Now,

In ∆TRS ,

$\angle TRS = 14 \degree \\ \angle TSR = 56 \degree \\ \angle RTS \ = m$

Since,

$\angle TRS \degree + \angle TSR \degree+\angle RTS \ = 180 \degree \\ (the \: sum \: of \: angles \: of \: triangle \: is \: 180 \degree)\\ 14 \degree + 56 \degree + m = 180 \degree \\ 70 \degree + m = 180 \degree \\ m = 180 \degree - 70 \degree \\m = 110 \degree$

Therefore,

$\angle m = 110 \degree$