Question

11 we dligles VI a qudurulu Three angles of a quadrilateral are in the ratio 3: 4: 5. If the fourth angle is 120°, find the other angles of the quadrilateral.​

Answer 1

Answer:

Answer

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Hint: Here, since angles are in the ratio 3: 5: 8, we can take the angles as 3x,5x and 8x. Next, with the help of formula of mean, sum of the values divided by the total number of values we can calculate the value of x. Now, with the help of x we can find three angles. To find the fourth angle we have to use the theorem that the sum of four angles of the quadrilateral is 360∘. Now, by solving we will get the fourth angle.

Complete step-by-step solution -

Here, for a better understanding, let us draw the figure.

We are given that three angles of a quadrilateral are in the ratio 3: 5: 8.

Therefore, let us take the three angles as 3x,5x and 8xrespectively.

Here, it is also given that the mean of these angles is 80∘.

We know by the definition of mean that:

mean=sum of the valuestotal number of values

mean=3x+5x+8x3

80=16x3 … (given that mean = 80)

Therefore, by cross multiplication, we get the equation:

80×3=16x240=16x

Now, by taking 16 to the left side we get:

24016=x15=x

Therefore, we got the value of x=15.

Now we have to find the three angles of the quadrilateral. i.e. 3x,5x and 8x. i.e.

3x=3×15=455x=5×15=758x=8×15=120

Hence, the three angles of the quadrilateral are 45∘,75∘ and 120∘.

Next, we have to find the fourth angle of the quadrilateral.

We know by a theorem that the sum of the four angles of a quadrilateral is 360∘.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let the measure of each of the equal angles be xWe know that, sum of four measure of angles of quadrilateral is 360 .⇒ 3x+4x+5x+120 =360

x+120 =360 ⇒ 12x+120 =360

x+120 =360 ⇒ 12x=240

x=240 ⇒ x=20

☞ hence 3x = 60

4x =80

5x=100

Hence, this is the answer.