1.

In the adjoining figure, ABC is a triangle in which side BC has been produced to D. If angle BAC =x°,angle ABC=(4a)°, angle BCA=a° and angle ACD=(5a)°, find the value of a and x.​

Answer»

In the given figure,

By LINEAR Pair of angles,

5A° + a° = 180°

⇒ 6a° = 180°

⇒ a = 180 ÷ 6

∴ a = 30°

In ΔABC,

By Angle Sum Property,

x° + 4a° + a° = 180°

⇒ x + 5a = 180°

⇒ x + 5(30) = 180°

⇒ x + 150° = 180°

⇒ x = 180° - 150°

∴ x = 30°

Confused? Let's Verify !!

By Angle Sum Property,

x + 4a + a = 180°

→ x + 5a = 180°

→ 30 + 5(30) = 180°

→ 30 + 150 =180°

→ 180° = 180°

LHS = RHS

★ Hence Verified ★

Know more:

  • Linear pair of angles STATES that Angles lying on a straight line sum up to 180°
  • Angle Sum Property states that Sum of all angles in a triangle sum up to 180°


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