If ABC is a right-angled triangle, what is the measure

Question

If ABC is a right-angled triangle, what is the measure of angle  \angle{ABC} ?

(A)  \angle{ABC}  is the largest angle.

(B)  \angle{BAC}=\angle{BCA}

Chetan's  questions

adstudy · Answer

As ABC is a right angled triangle, it means -

\angle{A}  +  \angle{B}  +  \angle{C}  = 180 ----- (1)
One of the angles is 90 degrees and that will be the largest angle ------- (2)

Statement A -  \angle{ABC}  is the largest angle.

From Line (2) and statement (A) we concur,

Measure of  \angle{ABC}  is 90 degree

Hence statement A is sufficient.

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Statement B -  \angle{BAC}=\angle{CBA}

From (2) we know,

One of the angles is 90 degree. So remaining two angle's sum will be 90 degrees (From Line 1)

Hence if

\angle{BAC}=\angle{CBA} , they cannot be both 90 degrees,

So Measure of  \angle{ABC}  has to be 90 degree

Hence statement B is sufficient.

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The answer then becomes D

CounterSniper · Answer

1. The largest angle of a rt angled triangle is 90=ABC
sufficient

2.both=45
ABC=90
sufficient

D

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