Question

1) In the given ABC; AB = BC and BD =

BC and BD = CD. Find the value
of a°, bº and cº.

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Answer 1

a = b = c = 45°

Explanation:

`In\: \triangle BDC, \\\\</p><p>BD = CD.... (given) \\\\</p><p>\therefore m\angle DBC =m\angle DCB\\(By\: isosceles \:\triangle\: property) \\</p><p>\therefore a\degree = b\degree.... (1)\\\\</p><p>m\angle BDC= 90\degree \\\\</p><p>\because m\angle BDC + a\degree + b\degree=180\degree \\\\</p><p>90\degree+ a\degree + a\degree=180\degree\\ [from \: equation \: (1)]\\\\</p><p></p><p>2a\degree=180\degree -90\degree\\</p><p>2a\degree= 90\degree\\\\</p><p>\therefore a\degree=( 90\degree)/(2) \\\\</p><p>\huge\purple {\boxed {\therefore a\degree=45\degree}} \\\\</p><p>\implies \huge\red {\boxed { b\degree=45\degree}} \\\\</p><p></p><p></p><p>In\: \triangle ABC, \\\\</p><p>AB = BC.... (given) \\\\</p><p>\therefore m\angle BAC =m\angle BCA\\(By\: isosceles \:\triangle\: property) \\</p><p>\therefore c\degree = b\degree\\\\</p><p>\because b\degree=45\degree \\\\</p><p>\implies \huge\orange {\boxed { b\degree=45\degree}} [`