Question

The measures of two adjacent angles of a parallelogram are in the ratio 4:5 . Find the measure of each of the angles of the parallelogram.

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Answer 1

Answer:

your answer buddy !!

Let ∠A and ∠B are two adjacent angles.

But we know that sum of adjacent angles of a parallelogram is 180

o

∠A+∠B=180

o

Given that adjacent angles of a parallelogram are in the ratio 4:5 and let that ratio be multiple of x

∠A+∠B=180

o

4x+5x=180

o

9x=180

o

x=180/9

x=20

o

∠A=4x=4×20=80

o

∠B=5x=5×20=100

o

Also ∠B+∠C=180

o

[Since ∠B and

∠C are adjacent angles]

100

o

+∠C=180

o

∠C=180

o

−100

o

=80

o

Now, ∠C+∠D=180

o

[Since ∠C and

∠D are adjacent angles]

80

o

+∠D=180

o

∠D=180

o

−80

o

=100

Hope this helps you ♡

mark as brainliest please ♡

Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

The measures of two adjacent angles of a parallelogram are in the ratio 4:5. Find the measure of each of the angles of the parallelogram.

$\large\underline{ \underline{ \sf \maltese{ \: Given:- }}}$

The measures of two adjacent angles of a parallelogram are in the ratio 4:5.

$\large\underline{ \underline{ \sf \maltese{ \: To \: Find :- }}}$

Find the measure of each of the angles of the parallelogram.

━━━━━━━━━━━━━━━━━━━━━━━━━

$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\boxed{ \sf \blue{ Suppose\: the \: angles \: be \: 4x \: and\: 5x }}$

$\boxed{ \sf \orange{ We \: have \: adjacent \: angles \: of \: a \: parallelogram \: = 180}}$

$\begin{gathered}\begin{gathered}\\ \sf \underline{ \green{putting \: all \: values : }}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\: \\ \sf \to \: 4x + 5x = 180\: \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:9x = 180 \\ \\ \: \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \frac{180}{9} \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \cancel{ \frac{180}{9} } \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \purple{x = 20}\\\\\end{gathered}\end{gathered}$

━━━━━━━━━━━━━━━━━━━━━━━━━

Measures of angles

$\begin{gathered}\begin{gathered}\sf \to \: 4x \\ \sf \to \: 4 \times 20 \\ \sf \to \red{80 }\\ \\ \\ \sf \to \: 5x \\ \sf \to \: 5 \times 20 \\ \sf \to \orange{100} \\\end{gathered}\end{gathered}$

━━━━━━━━━━━━━━━━━━━━━━━━━

$\large\underline{ \underline{ \sf \maltese{ \: Verification:- }}}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ 4x \: + \: 5x \: = \: 180 }} \\ \\ \qquad \quad {:}\longrightarrow\sf{\sf{4 \: \times 20 \: + \: 5 \times 100\: = \: 180 }} \\ \\ \qquad \quad {:}\longrightarrow\sf{\sf{ 80\: + \: 100 \: = \: 180 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ \:180° = \: 180° }}}$

Hence, Proved

━━━━━━━━━━━━━━━━━━━━━━━━━

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ measure \: of \: first \: angle \: = \underline {\underline{ \: 80 }}}\\\end{gathered}\end{gathered} \\ \begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ measure \: of \: second \: angle \: = \underline {\underline{ \: 100 }}}\\\end{gathered}\end{gathered}$