Question

The measures of two adjacent Angeles of parallelogram are in the ratio 5 : 1. Find the measure of each Angeles.​

Answer 1

Answer:

c) is the correct answer

Step-by-step explanation:

5a+1a=180°(adjacent angles)

6a=180°

a=180/6

a=30

=5×a=5×30=150°

=1×a=1×30=30°

Answer 2

$\large\blue{\underline{\underline{\sf{\purple{{Given \;that :-}}}}}}$

$↪$The measure of two adjacent angles of parallelogram are in the ratio 5 : 1

$\large\blue{\underline{\underline{\sf{\purple{{To \;Find:-}}}}}}$

$\sf↪ find \: the \: measure \: of \: each \: angeles \:$

$\large\blue{\underline{\underline{\sf{\purple{{Solution:-}}}}}}$

$\qquad \bf \:Let \: the \: parallelogram \: be \: \: ABCD$

$↪ \sf \red{ \qquad \: Given } \: adjacent \: angles \: are \: in \: the \: ratio \: 1 : 5$

$↪ \sf \: let \: these \: two \: angles \: be \: \angle A\: \: and \: \angle B\: \\ \\ \\ ↪\dfrac{\angle A }{\angle B}$

$\\ \green{\bf \: Let \: \angle A = 1x \: \: and \: \: \angle B = 5x}$

$\bf \: we \: know \: that \: :$

$\longrightarrow \boxed{ \sf \: {Adjacent \: angles \: of \: a \: parallelogram \: are \: supplementary }}$

According to the question

$\\ \tt\orange \longmapsto \: \angle A \: \: + \: \: \angle B \: \: = 180°$

putting values

$\\ \tt\orange \longmapsto1x \: \: + \: \: 5x \: \: = 180 \\ \\ \\ \\ \tt\orange \longmapsto 6x \: \: = 180° \\ \\ \\ \\ \tt\orange \longmapsto \: x \: \: = \: \: \cancel\dfrac{180°}{6} \\ \\ \\ \\ \tt\orange \longmapsto \frak{x \: \: = \: \: 30 °}$

Therefore,

The first angle A = 1x

$\\ \sf\orange \longrightarrow \angle A_{(parallelogram)}= 1x \\ \\ \\ \sf\orange \longrightarrow \angle A_{(parallelogram)}= 1(30) \\ \\ \\ \sf\orange \longrightarrow \angle \frak{A_{(parallelogram)}= 30°}$

and second angle B = 5x

$\\ \sf\orange \longrightarrow \angle B_{(parallelogram)}= 5x \\ \\ \\ \sf\orange \longrightarrow \angle B_{(parallelogram)}= 5(30)\\ \\ \\ \sf\orange \longrightarrow \angle \frak{B_{(parallelogram)}= 150°}$

Now,

$↪$Opposite angles of a parallelogram are equal

$\: \sf↪\angle C = \angle B = 30° \\ \bf \: and \\ \sf↪\angle B = \angle D = 150°$

_________________________

$\bf \: \huge \red{a)30°, 150°✔}$