Question

Two adjacent angles of parallelogram are (2y+10)° and (3y-40)°. Find the measure of all angles of the parallelogram. Answer:86°,94°​

Answer 1

Answer:

gg। hg f। h hg। g g hg। g

Step-by-step explanation:

g। g f f ggg g gf d। f f g g f f

Answer 2

Given :-

• Two adjacent angles of parallelogram are (2y+10)° and (3y-40)°

To Find :-

• All angles of the parallelogram

Formula Used :-

In parallelogram,

$⟼ \: \red{ \bf Sum \: of \: adjacent \: angles \: = \: 180 \degree}$

$⟼ \: \red{ \bf Sum \: of \: all \: angles \: = \: 360 \degree}$

Step-by-step Explanation :

Method - ❶

$⟼ \: \bf Sum \: of \: adjacent \: angles \: = \: 180 \degree$

$\: : \implies \: \: \sf \angle a \: + \: \angle b\: = \: 180 \degree$

$\: : \implies \: \: \sf (2y + 10) \: + \: (3y - 40)\: = \: 180 \degree$

$\: : \implies \: \: \sf 5y - 30\: = \: 180 \degree$

$\: : \implies \: \: \sf 5y\: = \: 180 + 30 \degree$

$\: : \implies \: \: \sf 5y \: = \: 210 \degree$

$\displaystyle\: : \implies \: \: \sf y \: = \: \cancel\frac{210}{5}$

$\displaystyle\: : \implies \: \: \bf y \: = \: 42$

Now,

$⟼ \: \: \sf \angle a \: = \: 2y + 10$

$\: : \implies \: \: \sf \angle a \: = \: 2(42) + 10$

$\: : \implies \: \: \sf \angle a \: = \: 84 + 10$

$\: : \implies \: \: \bf \angle a \: = \: 94 \degree$

And also,

$⟼ \: \: \sf \angle b \: = \: 3y - 40$

$\: : \implies \: \: \sf \angle b\: = \: 3(42) - 40$

$\: : \implies \: \: \sf \angle b \: = \: 126 - 40$

$\: : \implies \: \: \bf \angle b \: = \: 86 \degree$

Hence,

• ∠a = 94°
• ∠b = 86°

We also know that,

In parallelogram,

The adjacent angles are equal

So,

• ∠a & ∠c= 94°
• ∠b & ∠d = 86°

$\:$

Method - ❷

In parallelogram,

The adjacent angles are equal

So,

• ∠a & ∠c
• ∠b & ∠d

$⟼ \: \bf Sum \: of \: all \: angles \: = \: 360 \degree$

$\: : \implies \: \: \sf ∠a + ∠b + ∠c + ∠d \: = \: 360 \degree$

$\: : \implies \: \: \sf (2y + 10) + (3y - 40) + (2y + 10) + (3y - 40) \: = \: 360 \degree$

$\: : \implies \: \: \sf 2y + 10 + 3y - 40 + 2y + 10+ 3y - 40 \: = \: 360 \degree$

$\: : \implies \: \: \sf 10y +20 - 80 \: = \: 360 \degree$

$\: : \implies \: \: \sf 10y + (- 60)\: = \: 360 \degree$

$\: : \implies \: \: \sf 10y - 60\: = \: 360 \degree$

$\: : \implies \: \: \sf 10y \: = \: 360 + 60 \degree$

$\: : \implies \: \: \sf 10y \: = \: 420 \degree$

$\displaystyle \: : \implies \: \: \sf y \: = \: \cancel\frac{420 \degree}{10}$

$\displaystyle \: : \implies \: \: \bf y \: = \: 42\degree$

Now,

$⟼ \: \: \sf \angle a = \:\angle c \: = \: 2y + 10$

$\: : \implies \: \: \sf \angle a = \angle \: c \: = \: 2(42) + 10$

$\: : \implies \: \: \sf \angle a = \angle \: c \: _{(Parallelogam)} \: = \: 84+ 10$

$\: : \implies \: \: \bf \angle a = \angle \: c \: _{(Parallelogam)} \: = \: 94 \degree$

and also,

$⟼ \: \: \sf \angle b = \angle \: d \: = \: 3y - 40 \:$

$\: : \implies \: \: \sf \angle b = \angle d\: = \: 3(42) - 40$

$\: : \implies \: \: \sf \angle b = \angle d \: = \:12 6 - 40$

$\: : \implies \: \: \bf \angle b = \angle d \: = \:86 \degree$

Hence,

• ∠a & ∠c = 94°
• ∠b & ∠d = 86°

$\:$