Question

Two adjacent angles of a parallelogram are (3x - 4) and (3x + 16). Find the value of x a
find the measure of each of its angies.
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Answer 1

Step-by-step explanation:

Question :-

• Two adjacent angles of a parallelogram are (3x - 4) and (3x + 16). Find the value of x a
• find the measure of each of its angies.

Given :-

• Two adjacent angle of parallelogram ( 3x - 4 ) and ( 3x + 16 ) °

Solution :-

• Step 1

Apply the formula (3) to calculate the angles,

$Angle A+ Angle B = 180°$

• Step 2

Substitute the values,

$(3x − 4) + (3x + 16) = 180°$

• Step 3

Simplify the expression,

6x + 12° = 180°

6x = 180° - 12 °

6x = 168°

• Step 4

Divide both sides by 6,

$x = \frac{168°}{6}$

• Step 5

Cancel out the common term,

$x = 28°$

• Step 6

Substitute the value of x to find angle A,

$a \: = 3 \times 8 - 4 \\ = 84 - 4 \\ = 80°$

• Step 7

Substitute the value of x to find LB,

Angel b = 3 × 28 + 16

$= 84 + 16 \\ = 100 \: \: \: \: \: \: \: \:$

• Step 8

Apply the formula (2) to find Angle C,

Angle A = Angle C

• Step 9

Substitute the value of Angle A

$angle \: → c = 80°$

• Step 10

Apply the formula (2) to find Angle D,

Angle B = Angle D

• Step 11

Substitute the value of LB,

Angle D = 100°

So, Angle A = 80°, Angle B = 100°, Angle C = 80° and AngleD = 100°