Question

answer this question​

Answer 1

Φ = 20°

y = 65°

x = 25°

z = 50°

Answer 2

To Find:- θ, x, y, z

Given:- DEF is straight line, it is also a bisector of angle ∠ADB and AE = AF.

Solution:-

AE = AF .....given ...1

• Angle opposite to congruent sides are congruent.

•°• ∠AEF = ∠AFE i.e ∠AEF = y ........2

now, ∠AED + AEF = 180° ......straight line

115 + y = 180° ....from 2

y = 180 - 115

y = 65° .........3

•°• ∠AEF = y = 65° ........4

• now, In△AEF,

∠AFE + ∠AEF + ∠FAE = 180°

y + ∠AEF + z = 180°

y + y + z = 180 ........from 4

65 + 65 + z = 180

130 + z = 180

z = 180 - 130

z = 50° .........5

now, In △DBC , ∠DBC is 90°

∠DBC + ∠DCB + ∠BDC = 180°

90° + 70° + θ = 180°

θ = 180 - 160

θ = 20° .....6

now, In △DBE , ∠DBE = 90°

∠AEF = ∠DEB = 65° .....7..{vertically opposite angle}

∠DBE + ∠DEB + ∠BDE = 180°

90° + 65° + ∠BDE = 180°

155° + ∠BDE = 180°

∠BDE = 180 - 155

∠BDE = 25° ......8

now, ∠BDE = ∠ADE ......9..{°•° DF is bisector of angle ADB}

•°• ∠BDE = x = 25°

x = 25°

Answer ⬇️

θ = 20°, x = 25°, y = 65°, z = 50°