Question

If AB||CD , find the values of x,y and z.​

Answer 1

Step-by-step explanation:

$\Large \underline{\underline{\mathfrak{Solution \; (1) }}}$

Value of z :

$\longrightarrow \sf{\quad { z + 100^\circ = 180^\circ}}$

○ Reason : Sum of co-interior angles is 180°.

$\longrightarrow \sf{\quad { z = 180^\circ- 100^\circ}}$

Performing subtraction.

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ z = 80^\circ}}}}$

Value of y :

$\longrightarrow \sf{\quad { 70^\circ + y + z = 180^\circ}}$

○ Reason : Sum of all the angles that lie on the straight line is 180°.

Substitute the value of z.

$\longrightarrow \sf{\quad { 70^\circ + y + 80^\circ = 180^\circ}}$

Performing addition.

$\longrightarrow \sf{\quad { y + 150^\circ = 180^\circ}}$

Transposing 150 from LHS to RHS.

$\longrightarrow \sf{\quad { y = 180^\circ- 150^\circ}}$

Performing subtraction.

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ y = 30^\circ}}}}$

Value of x :

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ x = 70^\circ}}}}$

○ Reason : Alternate interior angles are equal. Here, x and 70° are alternate interior angles.

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

$\Large \underline{\underline{\mathfrak{Solution \; (2) }}}$

Value of y :

$\longrightarrow \sf{\quad { 80^\circ + 40^\circ+ y = 180^\circ}}$

○ Reason : Sum of the interior angles of triangle is 180°.

$\longrightarrow \sf{\quad { 120^\circ+ y = 180^\circ}}$

Transposing 120° form LHS to RHS.

$\longrightarrow \sf{\quad { y = 180^\circ- 120^\circ}}$

Performing subtraction.

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ y = 60^\circ}}}}$

Value of x :

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ x = 80^\circ}}}}$

○ Reason : Alternate interior angles are equal. Here, x and 80° are alternate interior angles.

Value of z :

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ y = 40^\circ}}}}$

○ Reason : Alternate interior angles are equal. Here, y and 40° are alternate interior angles.

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Answer 2

$\Large \underline{\underline{\mathfrak{Solution \; (1) }}}$

Value of z :

$\longrightarrow \sf{\quad { z + 100^\circ = 180^\circ}}$

○ Reason : Sum of co-interior angles is 180°.

$\longrightarrow \sf{\quad { z = 180^\circ- 100^\circ}}$

Performing subtraction.

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ z = 80^\circ}}}}$

Value of y :

$\longrightarrow \sf{\quad { 70^\circ + y + z = 180^\circ}}$

○ Reason : Sum of all the angles that lie on the straight line is 180°.

Substitute the value of z.

$\longrightarrow \sf{\quad { 70^\circ + y + 80^\circ = 180^\circ}}$

Performing addition.

$\longrightarrow \sf{\quad { y + 150^\circ = 180^\circ}}$

Transposing 150 from LHS to RHS.

$\longrightarrow \sf{\quad { y = 180^\circ- 150^\circ}}$

Performing subtraction.

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ y = 30^\circ}}}}$

Value of x :

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ x = 70^\circ}}}}$

○ Reason : Alternate interior angles are equal. Here, x and 70° are alternate interior angles.

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

$\Large \underline{\underline{\mathfrak{Solution \; (2) }}}$

Value of y :

$\longrightarrow \sf{\quad { 80^\circ + 40^\circ+ y = 180^\circ}}$

○ Reason : Sum of the interior angles of triangle is 180°.

$\longrightarrow \sf{\quad { 120^\circ+ y = 180^\circ}}$

Transposing 120° form LHS to RHS.

$\longrightarrow \sf{\quad { y = 180^\circ- 120^\circ}}$

Performing subtraction.

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ y = 60^\circ}}}}$

Value of x :

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ x = 80^\circ}}}}$

○ Reason : Alternate interior angles are equal. Here, x and 80° are alternate interior angles.

Value of z :

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{ y = 40^\circ}}}}$

○ Reason : Alternate interior angles are equal. Here, y and 40° are alternate interior angles.

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

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