Question

एका चौकोनाच्या चार कोनांची मापे अनुक्रमे (3x-15)°, (2x +10°), (4x-25)° व (x +30)° आहेत , तर त्या चौकोनाच्या सर्वात मोठ्या बाह्य कोनाचे माप किती ?
option: (1)98° (2) 119° (3)87° (4) 114°​

Answer 1

Given :- Four angles of a quadrilateral are (3x-15)°, (2x +10°), (4x-25)° and (x +30)° .

To Find :- Largest outside angle ?

Answer :-

we know that,

• sum of all angles of a quadrilateral is equal to 360° .

so,

→ (3x - 15)° + (2x + 10)° + (4x - 25)° + (x + 30)° = 360°

→ 3x + 2x + 4x + x - 15 + 10 - 25 + 30 = 360

→ 10x = 360

→ x = 36°

then,

→ Angle outside (3x - 15)° = 180° - (3x - 15°) = 180° - (3*36 - 15°) = 180° - (108° - 15°) = 180° - 93° = 87°

→ Angle outside (2x + 10)° = 180° - (2x + 10°) = 180° - (2*36 + 10°) = 180° - (72° + 15°) = 180° - 87° = 93°

→ Angle outside (4x - 25)° = 180° - (4x - 25°) = 180° - (4*36 - 25°) = 180° - (144° - 25°) = 180° - 119° = 61°

→ Angle outside (x + 30)° = 180° - (x + 30°) = 180° - (36° + 15°) = 180° - 51° = 129° = Largest angle. (Ans.)

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