Question

LINES AND ANGLES
Example 1 : In Fig. 6.9, lines PQ and RS
intersect each other at point O. If
Ent Z POR: ROQ = 5:7, find all the angles.

Answer 1

✯✯ QUESTION ✯✯

In Fig. 6.9, lines PQ and RS intersect each other at point O. If POR: ROQ = 5:7, find all the angles.

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✰✰ ANSWER ✰✰

$\longmapsto\tt{\angle{POR}+\angle{ROQ}=180\degree}$

$\longmapsto\tt{5x+7x=180\degree}$

$\longmapsto\tt{12x=180\degree}$

$\longmapsto\tt{x=\cancel\dfrac{180}{12}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{15}}}$

➥Now ,

$\longmapsto\tt{\angle{POR}=5x}$

$\longmapsto\tt{5\times{15}}$

$\longmapsto\tt\bold{75\degree}$

$\longmapsto\tt{\angle{ROQ}=7x}$

$\longmapsto\tt{7\times{15}}$

$\longmapsto\tt\bold{105\degree}$

➥So ,

$\longmapsto\tt{\angle{POS}=\angle{ROQ}}$ (V.O.A)

$\longmapsto\tt\bold{\angle{POS}=105\degree}$

➥Similarly : -

$\longmapsto\tt{\angle{SOQ}=\angle{POR}}$ (V.O.A)

$\longmapsto\tt\bold{\angle{SOQ}=180\degree}$

Answer 2

Answer:

Here is the answer

Step-by-step explanation:

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