in the given figure angle CAB : angle BAD = 1:2 find all the internal angles of ∆ ABC
Answers
Internal angles of ΔABC is 40°.
Given
To find all the internal angles of triangle ABC.
From the figure,
∠ABC = x
∠BCA = x+3
∠CAB : ∠ BAD = 1 : 2
Angle ∠CAB and ∠BAD are in the ratio of 1 : 2.
Sum of all angles is 180°.
∠ABC + ∠BCA + ∠CAB = 180°
x + x + 13° + ∠CAB = 180°
2x + 13° + ∠CAB = 180°
2x + ∠CAB = 180° - 13°
∠CAB = 167° - 2x
Also in supplementary,
∠CAB + ∠DAE + ∠BAD = 180°
( 167° - 2x ) + 60° + ∠BAD = 180°
167° -2x + ∠BAD = 180° - 60°
∠BAD = 120° - 167° + 2x
= 2x - 47°
∠BAD = 2x - 47°
Where, ∠CAB / ∠BAD = 1 / 2
substituting, ∠CAB and ∠BAD values, it gives
334° - 4x = 2x - 47°
334° + 47° = 2x + 4x
6x = 381°
x = (127 / 2)°
Angles of ΔABC,
∠ABC = x = (127 / 2)°
∠BCA = x+13°
= (127 / 2)° + 13°
= (153 / 2)°
∠CAB = 167° - 2x
= 167° - 2(127 / 2)°
= 40°
Therefore, internal angles of ΔABC is 40°.
To learn more...
brainly.in/question/2636506
