Question

Please help me out I am in a trouble.
kindly answer the question with explanation.
Thank you.

Answer 1

Answer:

Angle BOD= 50°

Angle AOD= 130°

Step-by-step explanation:

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Answer 2

$\large\boxed{\bf{\green{\underline{\underline{✤\</p><p>:GIVEN\:✤}}}}}$

$\bold\angle{AOC}=50°$

$\large\boxed{\bf{\green{\underline{\underline{✤\</p><p>:To\:Find\:✤}}}}}$

$\bold\angle{BOD}=?$

$\bold\angle{AOD}=?$

$\large\boxed{\bf{\green{\underline{\underline{✤\</p><p>:SOLUTION\:✤}}}}}$

AB and CD both are two straight lines.

We know that the sum of angles in a straight line is 180°

$\bold\angle{AOC}=50°$

So,

$\bold\angle</strong><strong>{</strong><strong>B</strong><strong>O</strong><strong>D</strong><strong>}</strong><strong>=5</strong><strong>0</strong><strong>°$ because it is vertically opposite angles.

$\bold\angle{AOC}+\angle{COB}=180°$

(sum of angles in a straight line is 180°)

Let $\bold\angle{COB\:be\:x}$

Therefore,

$\Longrightarrow\:50°+x=180°$

$\Longrightarrow</strong><strong>\</strong><strong>:</strong><strong>x=180°</strong><strong>-</strong><strong>5</strong><strong>0</strong><strong>°</strong><strong>$

$\Longrightarrow\:</strong><strong>x</strong><strong>=</strong><strong>1</strong><strong>3</strong><strong>0</strong><strong>°$

$\bold</strong><strong>\</strong><strong>t</strong><strong>h</strong><strong>e</strong><strong>r</strong><strong>e</strong><strong>f</strong><strong>o</strong><strong>r</strong><strong>e</strong><strong>\angle</strong><strong>{</strong><strong>C</strong><strong>O</strong><strong>B</strong><strong>}</strong><strong>=</strong><strong>1</strong><strong>3</strong><strong>0</strong><strong>°$

So, $\bold\angle</strong><strong>{</strong><strong>A</strong><strong>O</strong><strong>D</strong><strong>}</strong><strong>=</strong><strong>1</strong><strong>3</strong><strong>0</strong><strong>°$ because it is vertically opposite angles.

$\small{\sf{\green{\underline{\underline{✤\:ANSWERS\:ARE\:✤}}}}}$

$\bold\angle{AOD}=130°$

$\bold\angle{BOD}=50°$