Question

Consider the following parallelogram. Find the values of the unknowns x, y, z​

Answer 1

Step-by-step explanation:

Consider the following parallelograms. Find the values of the unknowns x, y, z

(i)

(ii)

(iii)

(iv)

(v)

Solution:

(i) \angle B+\angle C=180\degree∠B+∠C=180° [Supplementary angle theorem}

\therefore100\degree+x=180\degree∴100°+x=180° [Given]

x=180\degree-100\degreex=180°−100°

x=80\degreex=80°

(ii)

x+50\degree=180\degreex+50°=180°

[Adjacent angles in ||gm are supplementary]

\Rightarrow x=180\degree-50\degree=130\degree⇒x=180°−50°=130°

\Rightarrow z=x=130\degree⇒z=x=130°

[Corresponding angles]

(iii) x=90\degreex=90°

[Vertically opposite angles]

\Rightarrow y+x+30\degree=180\degree⇒y+x+30°=180°

[Angle sum property of a triangle]

\Rightarrow y+90\degree+30\degree=180\degree⇒y+90°+30°=180°

\Rightarrow y+120\degree=180\degree⇒y+120°=180°

\Rightarrow y=180\degree-120\degree=60\degree⇒y=180°−120°=60°

\Rightarrow z=y=60\degree⇒z=y=60°

[Alternate angles]

(iv) z=80\degreez=80°

[Corresponding angles]

\Rightarrow x+80\degree=180\degree⇒x+80°=180°

[Adjacent angles in a ||gm are supplementary]

\Rightarrow x=180\degree-80\degree=100\degree⇒x=180°−80°=100°

And y=80\degreey=80°

[Opposite angles are equal in a ||gm]

(v) y=112\degreey=112°

[Opposite angles are equal in ||gm]

\Rightarrow40\degree+112\degree+x=180\degree\Rightarrow152\degree+x=180\degree⇒40°+112°+x=180°⇒152°+x=180°

\Rightarrow x=180\degree-152\degree=28\degree⇒x=180°−152°=28°

And z=x=28\degreez=x=28°

[Alternate angles]

Answer 2

Answer:

Answer

(i) x+100=180 [Adjacent angles]

x=80

z=x=80∘[opposite angles are equal]

y=100∘

(ii) 50+y=180

y=130∘

x=y=130∘

and z=x=130∘(corresponding angles)

(iii) x=90∘

(vertically opposite angles)

x+y+30=180∘

y=180−120=60 ∘

z=y=60∘ (Alternate angles)

(iv) z=80,y=80 (Opposite angles)

x+y=180 ∘

,x=180−80⇒x=100 ∘

(v) y=112∘

(opposite angles)

x+y+40=180∘

(Angle sum property)

x=180°−152

x=28°

z=x=28° (alternative angles)