Question

5. The adjacent angles of a parallelogram
are in the ratio 4: 5. Find the measure of
all the angles of the parallelogram.​

Answer 1

Answer:

100°,80°,100°, and 80°

Step-by-step explanation:

4x + 5x = 180°  (sum of adjacent angles of a parallelogram is 180°)

= 9x = 180°

= x = 180/9

= x = 20

∠1 = 4 × 20 = 80°

∠2 = 5 × 20 = 100°

Hence, ∠1 = ∠3 = 80°    (opposite angles of a parallelogram are equal)

and ∠2 = ∠4 = 100°    (opposite angles of a parallelogram are equal)

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Answer 2

$\boxed{\red{AnswEr:-}}$

$\angle A$ = $\angle C$ = 80°

And, $\angle B$ = $\angle D$ = 100°

★ GivEn:-

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

★ To FinD :-

• The measurements of all the angles.

★ DiagrAm :-

$\setlength{\unitlength}{1cm}\thicklines \begin{picture}(10,10) \qbezier(0,0)(2.5,0)(5,0) \qbezier(0,0)(0.5,1.5)(1,3) \qbezier(5,0)(5.5,1.5)(6,3) \qbezier(1,3)(3,3)(6,3) \qbezier(0.6,0)(0.6,0.3)(0.2,0.6) \qbezier(0.8,2.4)(1.4,2.4)(1.6,3) \put(1.5,2.2){\huge{\textsf{4x}}} \put(0.3,0.3){ \huge{ \textsf{5x}}} \put( - 0.5, - 0.5){ \huge{B}}\put(5, - 0.5){ \huge{C}}\put(0.5, 3.3){ \huge{A}}\put( 6, 3.3){ \huge{D}}\end{picture}$

★ SoluTiOn :-

➟ Let the common factor of the ratio be x ( x > 0)

➟ So, The adjacent angles of the parallelogram would be 4x and 5x respectively.

➟ We know, the sum of two adjacent angles of a parallelogram is 180°

➟ Therefore,

$4x + 5x = 180 \\ \\ = > 9x = 180 \\ \\ = > x = \frac{180}{9} = 20$

➟ The adjacent angles are (20 × 4) = 80° and (20 × 5) = 100° respectively.

$\angle A$ = 80°

$\angle B$ = 100°

➟ We know that, the opposite angles of a parallelogram are equal.

So, $\angle A$ = $\angle C$ = 80°

And, $\angle B$ = $\angle D$ = 100°

➟ The total sum of the angles,

80° + 100° + 80° + 100° = 360°

➟ Hence, it is verified.