Question

Two opposite angles of a parallelogram are (2x 10)° and (50 3x)°. Find the measures of each of angle of the parallelogram.​

Answer 1

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

Two opposite angles of a parallelogram are (2x-10)° and (50-3x)°. Find the measures of each angle of the parallelogram.

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

Measurements of each angles of the parallelogram are 14° , 14° , 166° and 166° .

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

Two opposite angles of a parallelogram are (2x-10)° and (50-3x)° .

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

Find the measures of each angle of the parallelogram.

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

We know that opposite angles of parallelogram are equal . Therefore ,

$\displaystyle \bf \implies2x - 10 = 50 - 3x \\ \\ \displaystyle \bf \implies2x + 3x = 50 + 10 \\ \\ \displaystyle \bf \implies5x = 60 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \bf \implies x = \frac{60}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \bf \implies x = 12 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \boxed{\begin{array}{l} \bf(2x - 10) \degree = (24 - 10) \degree = 14 \degree \\ \\ \bf(50 - 3x) \degree =(50 - 36) \degree = 14\degree \end{array}}}$

We know that adjacent angles of parallelogram are equal to 180 ° . Therefore ,

Let adjacent angles as " a " .

Since both angles are parallel to each other , therefore they are also equal .

$\displaystyle \bf \implies 14 \degree + a = 180\degree \: \\ \\ \displaystyle \bf \implies a = 180\degree - 14 \degree \\ \\ \displaystyle \bf \implies a = 166\degree \: \: \: \: \: \: \: \: \: \: \: \:$

Other two angles are 166° each .

$\green{ \large \underline{ \mathbb{\underline{VERIFICATION : }}}}$

We know that sum of all angles of parallelogram is equal to 360° .

$\displaystyle \bf \implies14\degree + 14 \degree+ 166\degree + 166\degree = 360 \degree \\ \\ \displaystyle \bf \implies28\degree + 332\degree = 360 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \bf \implies360 \degree = 360 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence , Verified .

$\green{ \large \underline{ \mathbb{\underline{KNOW\:MORE : }}}}$

$\purple{ \boxed{ \begin{array}{l} \green{\mathbb{ \underline{\underline{PROPERTIES \: OF \: PARALLELOGRAM:}}}} \\ \\ \bullet \: \textsf {The opposite sides are parallel and equal}. \\ \\ \bullet \textsf{The opposite angles are equal .} \\ \\ \bullet \textsf{The adjacent angles are supplementary .}\\ \\ \bullet \: \textsf{If any one of the angles is a right angle, then all the other angles will be at right angle.} \\ \\ \bullet \: \textsf{The two diagonals bisect each other.} \\ \\ \bullet \: \textsf{Each diagonal bisects the parallelogram into two congruent triangles .}\\ \\ \bullet \: \textsf{Sum of square of all the sides of parallelogram is equal to the sum of square of its diagonals.}\end{array}}}$