Question

please solve this very urgent​

Answer 1

Step-by-step explanation:

Solutions:-

Figure -1:-

Points A,O and B are collinear.

<BOC+ <COD + <DOA = 180°

=>x+5°+4x-25°+x-10° = 180°

=> 6x-30° = 180°

=> 6x = 180°+30°

=> 6x = 210°

=> x = 210°/6

=> x = 35°

The value of x = 35°

Now, <BOC = x+5° = 35°+5° = 40°

The measure of the angle BOC = 40°

Figure -2:-

l and m are parallel lines and s is a transversal then

a+ b and 65° are interior angles on the same side to the transversal

We know that

They are supplementary angles.

=> a+b+65° = 180°

=> a+b = 180°-65°

=> a+b = 115° ---------------(1)

l and m are parallel lines and t is a transversal then

b and 132° are interior angles on the same side to the transversal

We know that

They are supplementary angles.

=>b+132° = 180°

=>b = 180°-132°

=> b = 48°

On Substituting the value of b in (1) then

=> a+48° = 115°

=> a = 115°-48°

=> a = 67°

The values of a and b are 67° and 48° respectively.

3)Let the other angle be X°

Then one of the angles = one third of the other

=> (1/3)×X°

=> X°/3

Since they form a linear pair then

Their sum = 180°

=> X°/3 + X° = 180°

=> (X°+3X°)/3 = 180°

=> 4X°/3 = 180°

=> 4X° = 180°×3

=> 4X° = 540°

=> X° = 540°/4

=> X° = 135°

Other angle = 135°

One of the angles = 135°/3 = 45°

The two angles are 45° and 135°

Used formulae:-

• The interior angles on the same side to the transversal are supplementary.
• The sum of two adjacent angles is supplementary then they are called Linear pair.