Question

16In the given fig.,BAC is a line. Find X Hence find angleCAE and angleBAD​

Answer 1

GIVEN :-

• BAC is a line.
• ∠CAE = (3x - 5)°
• ∠EAD = 55°.
• ∠BAD = (x + 20)°

TO FIND :-

• the value of x and the value of ∠CAE and ∠BAD .

SOLUTION :-

$\\ : \implies \displaystyle \sf \: \angle CAE + \angle BAD + \angle EAD = 180 ^{ \circ} \: \: \: \: \: \: \: \: \: \: \bigg \lgroup\because \: linear \: pair \bigg \rgroup$

$: \implies \displaystyle \sf \: (3x - 5) ^{ \circ} + (x + 20) ^{ \circ} + 55 ^{ \circ} = 180 ^{ \circ}$

$: \implies \displaystyle \sf \: 3x - 5 + x + 20 + 55 = 180$

$: \implies \displaystyle \sf \: 3x + x + 20 - 5 + 55 = 180$

$: \implies \displaystyle \sf \: 4x + 75 - 5 = 180$

$: \implies \displaystyle \sf \: 4x + 70 = 180$

$: \implies \displaystyle \sf \: 4x = 180 - 70$

$: \implies \displaystyle \sf \: 4x = 110$

$: \implies \displaystyle \sf \: x = \frac{110}{4}$

$: \implies \underline{ \boxed{ \displaystyle \sf \: x = 27.5}}$

Now put the value of x in ∠CAE and ∠BAD.

$\\ \\ : \implies \displaystyle \sf \: \angle CAE = (3x - 5) ^{ \circ}$

$: \implies \displaystyle \sf \: \angle CAE = (3 \times 27.5 - 5) ^{ \circ}$

$: \implies \displaystyle \sf \: \angle CAE = (82.5 - 5) ^{ \circ}$

$: \implies \underline{ \boxed{\displaystyle \sf \: \angle CAE = 77.5 ^{ \circ} }}$

Similarly,

$\\ \\ : \implies \displaystyle \sf \: \angle BAD = (x + 20) ^{ \circ}$

$: \implies \displaystyle \sf \: \angle BAD = (27.5 + 20) ^{ \circ}$

$: \implies \underline{ \boxed{\displaystyle \sf \: \angle BAD = 47.5^{ \circ} }}$

Answer 2

$\huge\underline\mathfrak\red{Answer}$

Given that -

• BAC is a line
• Angle EAD = 55°
• Angle CAE = (3x-5)°
• Angle BAD = (x+20°)

To find -

• The value of x and the value of Angle CAE and Angle BAD.

Solution -

• Angle CAE + Angle BAD + Angle EAD = 180° { Linear Pair }
• ( 3x - 5° ) + ( x + 20° ) + 55° = 180°
• 3x - 5 + x + 20 + 55 = 180
• 3x + x + 20 - 5 + 55 = 180°
• 4x + 75 - 5 = 180°
• 4x + 70 = 180°
• 4x = 180 - 70
• 4x = 110°
• x = 110 / 4
• x = 27.5

Now put the value of x in Angle CAE and in Angle BAD .

• Angle CAE = (3x+5)°
• Angle CAE = (3 × 27.5 - 5)°
• Angle CAE = (82.5 - 5)°
• Angle CAE = 77.5 °

Similarly,

• Angle BAD = (x+20)°
• Angle BAD = (27.5 + 20)°
• Angle BAD = 47.5°

So,

• The value of x = 27.5 degree
• The value of BAD = 47.5 degree
• The value of CAE = 77.5 degree

Hope it's helpful

Thank you :)