Question

Considered the following parallelograms. Find the values of the unknown x,y,z .

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Answer 1

Answer:

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1 . angle D =angle B (vertically opposite angles)

angle D=100

y =100

angle D +angle A=180

y+z=180

z=180-100

z=80

angle A=angle C

z=x

x=80

Answer 2

Step-by-step explanation:

(1) /B = /D [Opposite angles of parallelogram are equal]

/D = 100⁰

/C + /B = 180⁰

/C + 100⁰ =180⁰

/C = 80⁰

/C = /A = 80⁰

(2) z = 180⁰- 50⁰

z = 130⁰

y = z [Alternative angles]

y = 130⁰

y = x = 130⁰ [Opposite angles of parallelogram are equal]

3) x = 90⁰ [Vertically opposite angles are equal]

x+y+30⁰ = 180⁰ [Angle sum property]

y = 60⁰

y = z = 60⁰ [Alternative angles]

4) y = 80⁰ [Opposite angles of parallelogram are equal]

y = z = 80⁰ [Alternative angles]

x+y = 180⁰ [Corresponding angles]

x = 100⁰

5) y= 112⁰ [Opposite angles of parallelogram are equal]

x+y+40⁰ = 180⁰ [Angle sum property]

x = 28⁰

x=z [Alternative angles]

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