Question

FIND THE MEASURE ANGLE OF BOC,COD and DOE

Answer 1

Step-by-step explanation:

Solution :-

From the given figure :

<AOB = 50°

<BOC = x+10°

<COD = 2x+30°

<DOE = 2x-10°

We know that

The sum of the angles lie on the same line = 180°

=> <AOB + <BOC + <COD + <DOE = 180°

=> 50°+x+10°+2x+30°+2x-10° = 180°

=> 5x+80° = 180°

=> 5x = 180°-80°

=> 5x = 100°

=> x = 100°/5

=> x = 20°

Therefore, x = 20°

Now,

The measure of <BOC = x+10°

= 20°+10°

= 30°

The measure of <COD = 2x+30°

= 2(20°)+30°

= 40°+30°

= 70°

The measure of <DOE = 2x-10°

=2(20°)-10°

= 40°-10°

= 30°

Answer:-

The measure of <BOC = 30°

The measure of <COD = 70°

The measure of <DOE = 30°

Used formulae:-

→ The sum of the angles lie on the same line is 180°