Question

Two adjacent angles of the parallelogram are (3a +10)° and (3a-4)°. Find the value of a? *

Answer 1

GIVEN:

• Two adjacent angles of the parallelogram are (3a +10)° and (3a-4)°

TO FIND:

• What is the value of a ?

SOLUTION:

We have given that two adjacent angles of the parallelogram are (3a +10)° and (3a-4)°

We know that the sum of adjacent angles is 180°

According to question:-

$\rm{\implies (3a + 10) + (3a -4) = 180\degree}$

$\rm{\implies 6a + 6 = 180\degree}$

$\rm{\implies 6a = 180-6}$

$\rm{\implies 6a = 174}$

$\rm{\implies a = \cancel\dfrac{174}{6}}$

$\bf{\implies \star \: a = 29 \: \star }$

Measure of angles:

➠ $\rm{ 3 \times 29 + 10 = 97\degree}$

➠ $\rm{ 3 \times 29 - 4 = 83\degree}$

VERIFICATION:

➠ 97 + 83 = 180°

➠ 180° = 180°

VERIFIED....

____________________

Answer 2

✯✯ QUESTION ✯✯

Two adjacent angles of the parallelogram are (3a +10)° and (3a-4)°. Find the value of a?

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✰✰ ANSWER ✰✰

$\longrightarrow{1st\:Adjacent\:Angle=(3a+10)}$

$\longrightarrow{2nd\:Adjacent\:Angle=(3a-4)}$

Now ,

Sum of Adjacent Angles of the Parallelogram is 180°..

A.T.Q : -

$\longrightarrow{3a+10+3a-4=180}$

$\longrightarrow{3a+3a+10-4=180}$

$\longrightarrow{6a+10-4=180}$

$\longrightarrow{6a+6=180}$

$\longrightarrow{6a=180-6}$

$\longrightarrow{a=\cancel\dfrac{174}{6}}$

$\longrightarrow{\large{\boxed{\bold{\bold{\red{\sf{a=29}}}}}}}$

➥So,The value of a is 29..

So ,

$\longrightarrow{1st\:Angle=3(29)+10)}$

$\longrightarrow{\textbf{97\degree}}$

$\longrightarrow{2nd\:Angle=3(29)-4}$

$\longrightarrow{\textbf{83\degree}}$

VERIFICATION : -

$\longrightarrow{1st\:Angle+2nd\:Angle=180\degree}$

$\longrightarrow{97\degree+83\degree=180\degree}$

$\longrightarrow{180\degree=180\degree}$

✺ HENCE VERIFIED ✺