GEOMETRY

Geometry Level 1

ABCD is a rhombus and ∠ACB = 45°, Find ∠ADC.

110° 100° 120° 90°

Akash Dhasmana by akash dhasmana , 20, India

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5 solutions

Edwin Gray
Sep 12, 2018

Draw the diagonal AC. Given that <ACB = 45, and BC = AB since the figure is a rhombus. Then < BAC = 45, since triangle ABC is isosceles. This means that <ABC = 90, since the sum of angles = 180. Furthermore , triangle ABC is congruent to triangle ACD, and < ADC = 90 by corresponding parts. Ed Gray

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Walid Afifi
Mar 22, 2014

each angle of rhombus equals to 90

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each angle of a rhombus isnt 90 degrees. a rhombus with all angles equal to 90 degrees is called a square!

Baidehi Chattopadhyay - 7 years, 1 month ago

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Wrong

Atul Chaudhary - 7 years, 1 month ago

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Why wrong? I just saw that in my comment instead of 90 degrees i had written 9- degrees but that was a typing mistake. anything else wrong?

Baidehi Chattopadhyay - 7 years, 1 month ago

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@Baidehi Chattopadhyay – The square is a kind of rhombus whose all angles equal 90 degrees.

د. خالد لاشين - 6 years, 12 months ago

Each angle of all rhombus are not equal to 90. Rhombus means a parallelogram having all sides of equal length.

Smit Kiri - 7 years, 1 month ago

true

Punith Bajaj - 7 years, 1 month ago

" each angle of rhombus equals to 90 " is a square

Yitong Yab - 6 years, 11 months ago

The given is incomplete. So theoretically, all answers are correct. Try drawing it with all the answers. You can get a rhombus with all of those angles.

Dave Solis - 6 years, 10 months ago

the difference between a rhombus and a square is square equals to 90 degree at each side while rhombus has same length at each sides but different in angles . Another name for rhombus is equilateral quadrilateral .

Yitong Yab - 6 years, 11 months ago
Saurabh Jha
Mar 22, 2014

in rhombus diagonals bisect the angel at vertices...so its angle will be 90...therefore the answer is 90

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Vinayak Rastogi
Mar 1, 2014

its because the diagonal of a rhombus bisects the angles at the vertices, and the 2 adjacent angles are in a rhombus are supplementary. skadoosh!!!! :D

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i have just gambled it.

Tamanna S Mohanty - 7 years, 2 months ago

it's definitely 90 degree

Tanjil Islam - 7 years, 2 months ago
Shreya R
Feb 27, 2014

Rhombus is a parallelogram with all angles= 90 degrees

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each angle of rhombus does not equal to 90

divyansh mehrotra - 7 years, 3 months ago

You are wrong. That is known as a square or a rectangle

Kushagra Sahni - 7 years, 3 months ago

Square is a special case of a rhombus, a rhombus does not have all angles equal to 90 degrees.

Baidehi Chattopadhyay - 7 years, 1 month ago

Rhombus is a parallelogram whose all sides are equal. And the square is a rectangle whose all sides are equal or a rhombus whose all angles= 90 degrees.

د. خالد لاشين - 6 years, 12 months ago

then how come ACB=45

Abin Jacob - 7 years, 3 months ago

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Within the Rhombus there are 2 triangles ABC & ADC. If ∠ACB is 45° that means ∠C for Rhombus = ∠ACB * 2 (since all sides are equal),which is 90°. Rhombus with 90° angle will be a square. Hence, ∠ADC will be 90°.

Saurabh Trivedi - 7 years, 1 month ago

this rhombus is not parallelogram but its square

Saurabh Jha - 7 years, 2 months ago

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