Question

PLEASE ANSWER WITH BRIEF EXPLANATION​

Answer 1

Answer:

150+x+60=360

x+210=360

x=210-360

=-150

Answer 2

Question: In the given figure, if ∠CAD = 150° and ∠ABC = 60°, then reflex of ∠ACB is _______

Given:

∠CAD = 150°

∠ABC = 60°

To Find:

Reflex of angle ∠ACB

Solution:

∠DAC + ∠BAC = 180° [Linear Pair]

150° + ∠BAC = 180°

∠BAC = 180° - 150°

∠BAC = 30°

In ΔABC,

∠BAC + ∠ABC + ∠BCA = 180° [ASP of a Triangle]

30° + 60° + ∠BCA = 180°

90° + ∠BCA = 180°

∠BCA = 180° - 90°

∠BCA  = 90°

Reflex of an angle means the angle subtracted by the complete angle, i.e, 360°. [More about reflex angles at the end.]

∴ Reflex of Angle ACB is,

Here, R∠ACB stands for 'Reflex of ∠ACB' it differentiate it from ∠ACB

R∠ACB = 360° - ∠ACB

R∠ACB = 360° - 90°

R∠ACB = 270°

∴ Reflex of ∠ACB is 270°

________________________________________

Reflex Angles.

→ Reflex angles are greater than 180° and less than 360°.

→ Reflex of an angle is the angle subtracted from 360°.