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Question

In theis diagram AB=AC angle A = 40 degree and BD is perpendicular to AC at D. how many degrees are there in angle DBC?

20 degree

40 degree

50 degree

70 degree

ANSWER : 1

Descrption

<pre><math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>△</mo><mi>A</mi><mi>B</mi><mi>C</mi><mo> </mo><mi>এ</mi><mo> </mo><mi>A</mi><mi>B</mi><mo> = </mo><mi>A</mi><mi>C</mi><mo>,</mo><mo>∠</mo><mi>B</mi><mo> = </mo><mo>∠</mo><mi>C</mi><mspace linebreak = "newline"/><mo>∴</mo><mo>∠</mo><mi>A</mi><mo>  +  </mo><mo>∠</mo><mi>B</mi><mo>  +  </mo><mo>∠</mo><mi>C</mi><mo> = </mo><msup><mn>180</mn><mo>∘</mo></msup><mspace linebreak = "newline"/><mo>⇒</mo><mo>∠</mo><mi>B</mi><mo>  +  </mo><mo>∠</mo><mi>C</mi><mo> = </mo><msup><mn>180</mn><mo>∘</mo></msup><mo> - </mo><msup><mn>40</mn><mo>∘</mo></msup><mspace linebreak = "newline"/><mo>⇒</mo><mo>∠</mo><mi>B</mi><mo>  +  </mo><mo>∠</mo><mi>C</mi><mo> = </mo><msup><mn>140</mn><mo>∘</mo></msup><mspace linebreak = "newline"/><mo>⇒</mo><mn>2</mn><mo>∠</mo><mi>B</mi><mo> = </mo><msup><mn>140</mn><mo>∘</mo></msup><mspace linebreak = "newline"/><mo>∴</mo><mo>∠</mo><mi>B</mi><mo> = </mo><msup><mn>70</mn><mo>∘</mo></msup><mo> = </mo><mo>∠</mo><mi>C</mi><mspace linebreak = "newline"/><mi>A</mi><mi>g</mi><mi>a</mi><mi>i</mi><mi>n</mi><mo>,</mo><mo> </mo><mo>△</mo><mi>A</mi><mi>B</mi><mi>D</mi><mo> </mo><mi>এ</mi><mo> </mo><mo>∠</mo><mi>A</mi><mi>D</mi><mi>B</mi><mo> = </mo><msup><mn>90</mn><mo>∘</mo></msup><mspace linebreak = "newline"/><mo>∠</mo><mi>A</mi><mo> = </mo><msup><mn>40</mn><mo>∘</mo></msup><mspace linebreak = "newline"/><mo>∴</mo><mo>∠</mo><mi>D</mi><mi>B</mi><mi>A</mi><mo> = </mo><msup><mn>180</mn><mo>∘</mo></msup><mo> - </mo><msup><mn>90</mn><mo>∘</mo></msup><mo> - </mo><msup><mn>40</mn><mo>∘</mo></msup><mo> = </mo><msup><mn>50</mn><mo>∘</mo></msup></math>
<math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>&#x2234;</mo><mo>&#x2220;</mo><mi>D</mi><mi>B</mi><mi>C</mi><mo> = </mo><mo>&#x2220;</mo><mi>A</mi><mi>B</mi><mi>C</mi><mo> - </mo><mo>&#x2220;</mo><mi>D</mi><mi>B</mi><mi>A</mi><mo> = </mo><msup><mn>70</mn><mo>&#x2218;</mo></msup><mo> - </mo><msup><mn>50</mn><mo>&#x2218;</mo></msup><mo> = </mo><msup><mn>20</mn><mo>&#x2218;</mo></msup></math>
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