Question

Find the angle measures of x, y, z.​

Answer 1

With the view on point D, we get

50° + Y° + X° = 180°

(Angles on a straight line)

As ∆BDC has external angle of 110° at point C,

X° + 30°=110°

(External angle = summation of angle except the internal one)

In ∆ABD,

80° + Y° + Z° = 180°

(Summation of the Angles in a Triangle)

In the rectangle ABCD

( X° +Y° ) + 80° + ( Z° + 30° ) + ( 180° - 110° ) = 360°

or, X° + Y° + Z° = 180°

(All the angles of Rectangle)

Solving All the derived formula we get,

X=80°

Y=50°

Z=50°

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Answer 2

GIVEN :

• ∠BAD = 80° , ∠DBC = 30° , ∠BCF = 110° , ∠ADE = 50°

TO FIND :

• ∠ADB , ∠BDC , ∠ABD

SOLUTION :

∠BCD + ∠BCF = 180° { ∵ ANGLES ON STRAIGHT LINE }

=> ∠BCD + 110° = 180°

=> ∠BCD = 70°

NOW IN ΔBDC ,

∠BCD + ∠DBC + ∠BDC = 180° { ∵ ANGLE SUM PROPERTY }

=> 70° + 30° + x° = 180°

=> 100° + x° = 180°

=> x = 80°

NOW ,

∠ADE + ∠ADB + ∠BDC = 180° { ANGLES ON STRAIGHT LINE }

=> 50° + y + 80°

=> y = 30°

IN ΔABD ,

∠ABD + ∠ADB + ∠BAD = 180° { ∵ ANGLE SUM PROPERTY }

=> z + 80° + 30° = 180°

=> z = 70°

∴ X = 80° , Y = 30° , Z = 70°

HOPE IT HELPS !!!!