Question

In the given figure, find the measure of angle BOC, angle COD and angle DOE ?​

Answer 1

Answer:

Step-by-step explanation:

$2x - 10^o + 2x + 30^o + x + 10^o + 50^o = 180^o \\\ 5x + 80^o = 180^o \\\ 5x = 180^o - 80^o \\\ 5x = 100^o \\\ x = \frac{100^o}{5} \\\\ x = 20°$

I hope I've helped you.

Answer 2

Explanation:-

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°

∴ 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°

Remember:-The sum of the angles lie on the same line is 180°