Question

what are values of the two angles shown in the given figure below ​

Answer 1

Answer:

The answer is 30° and 90°

Step-by-step explanation:

3x°+12x-30°=180°. (Linear pair)

15x-30°=180°

15x=180-30

x=150°/15

x=10°

Therefore, the angles are 3x=3×10°=30° and 12x-30=12×10-30=120-30=90°

30° and 90°

Answer 2

Angles are $42^{o}$ and $138^{o}$.

Step-by-step explanation:

Given:

Angle 1 $= 3x^{o}$

Angle 2 $= 12x-30^{o}$

To Find:

Value of $x$

Calculation:

• When two lines intersect as shown in figure, there are angles formed. Two adjacent angles are called linear pair angles.

• Adjacent angles are formed when two angles have a common vertex and a common arm but do not overlap.

• The linear pair of angles are always supplementary as they form on a straight line.

Supplementary angles sum up to $180^{o}$.

So,

$(3x)^{o} +(12x-30)^{o} = 180^{o} \\15x-30=180^{o}\\15x=210^{o}\\x=14$

Since value of $x$ is $14$.

Therefore Angle 1 $=3x=3*14=42^{o}$

Angle 2 $=12x-30=12*14-30=138^{o}$