Question

Construct a parallelogram HEAR where
$HE = 5cm \\ \ \textless \ br /\ \textgreater \ EA = 6cm \\ \angle \: R = 85 \degree$
​

Answer 1

Given ↴

➥ Construct a parallelogram HEAR where $\begin{gathered}HE = 5cm \\ EA = 6cm \\ \angle \: R = 85 \degree\end{gathered}$

Calculation ↴

$\angle \: E \: = \angle\:R \: (\because \: opposite \: angles \: of \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: a \: parallelogram \: are \: equal)\\ \therefore \angle \: E = 85 \degree \\ Also \: ,\angle \: A + \angle \: R = 180 \degree \: ( \because \: Adjacent \: angles \: of \: a \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: parallelogram \: are \: supplementary \: ) \\ \therefore \angle \: A + 85 \degree \: = 180 \degree \\ \therefore \angle \: A = 180 \degree - 85 \degree \\ \therefore \angle \: A = 95 \degree \\ Further , \\ \: \: \: \: \: \: \: \: \: \: \: AR = HE \: ( \because \: opposite \: sides \: of \: a \\ \: parallelogram \: are \: equal)$

Step of construction ↴

• ➥ Draw EA = 6 cm
• ➥Draw $\angle XEA = 85°$
• ➥Draw $\angle YAE = 95°$
• ➥Locate point H on the ray EX such that EH = 5 cm
• ➥Locate point R on the ray AY such that AR = 5 cm
• ➥Complete HEAR
• ➥Thus , HEAR is the required parallelogram.

NOTE : For construction refer the attachment.

Answer 2

Answer:

Construct a parallelogram HEAR where \begin{gathered}\begin{gathered}HE = 5cm \\ EA = 6cm \\ \angle \: R = 85 \degree\end{gathered} \end{gathered}

HE=5cm

EA=6cm

∠R=85°

Calculation ↴

\begin{gathered} \angle \: E \: = \angle\:R \: (\because \: opposite \: angles \: of \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: a \: parallelogram \: are \: equal)\\ \therefore \angle \: E = 85 \degree \\ Also \: ,\angle \: A + \angle \: R = 180 \degree \: ( \because \: Adjacent \: angles \: of \: a \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: parallelogram \: are \: supplementary \: ) \\ \therefore \angle \: A + 85 \degree \: = 180 \degree \\ \therefore \angle \: A = 180 \degree - 85 \degree \\ \therefore \angle \: A = 95 \degree \\ Further , \\ \: \: \: \: \: \: \: \: \: \: \: AR = HE \: ( \because \: opposite \: sides \: of \: a \\ \: parallelogram \: are \: equal)\end{gathered}

∠E=∠R(∵oppositeanglesof

aparallelogramareequal)

∴∠E=85°

Also,∠A+∠R=180°(∵Adjacentanglesofa

parallelogramaresupplementary)

∴∠A+85°=180°

∴∠A=180°−85°

∴∠A=95°

Further,

AR=HE(∵oppositesidesofa

parallelogramareequal)

Step of construction ↴

➥ Draw EA = 6 cm

➥Draw \angle XEA = 85°∠XEA=85°

➥Draw \angle YAE = 95°∠YAE=95°

➥Locate point H on the ray EX such that EH = 5 cm

➥Locate point R on the ray AY such that AR = 5 cm

➥Complete HEAR

➥Thus , HEAR is the required parallelogram.

NOTE : For construction refer the attachment.