Question

in the adjoining figure aob is a straight line if x:y:z=4:5:6 then y
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Answer 1

The value of y is 60°.

Option (a) is correct.

Step-by-step explanation:

Given:

• A figure. (Attached)
• A straight line AOB.
• Ratio of angles x:y:z=4:5:6

To find:

• Find the value of y.
• a) 60°
• b) 80°
• c) 48°
• d) 72°

Solution:

Theorem/Concept to be used:

• Sum of all angles on a straight line is 180°.
• Assume a common factor of all angles and find the value of that factor.

Step 1:

Find the common factor of ratios.

Let the common factor of ratios is k.

So,

$4k + 5k + 6k = {180}^{ \circ}$

or

$15k = {180}^{ \circ}$

or

$k = \frac{ {180}^{ \circ}}{15}$

or

$\bf \red{k = 12}$

Step 2:

Find the value of angle y.

Multiply the common factor with ratio of angle y.

$y = 5 \times 12$

or

$\bf \red{y = {60}^{ \circ} }$

Thus,

Value of y is 60°.

Option (a) is correct.

Learn more:

1) find angle x and y in figure

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2) Value of x in the figure below is:

х

100°

60°

a) 20°

b) 40°

c) 80°

d) 160°

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