Question

How do you find the measures of angles in a rhombus?

Answer 1

Hint: This question is from the topic of geometry. In solving this question, we will first draw a figure of rhombus. After that, we will see the properties of rhombus. After that, we will assume any one interior angle of rhombus as \[\theta \]. After that, we will find the other three interior angles of the rhombus.

Complete step-by-step answer:
Let us solve this question.
In this question, we have asked that how do we find the measures of angles in a rhombus. That means, we will understand how to find the interior angles of a rhombus.
Let us first understand from a figure that what a rhombus is.
The figure for rhombus is in the following:

Now, let us know about the properties of rhombus.
The properties of rhombus are:
1) All sides of a rhombus are equal. (From the figure, we can say that \[AB=AC=CD=BD\])
2) The opposite sides of a rhombus are parallel.
3) Diagonals of a rhombus bisect each other at 90 degrees. Diagonals bisect the interior angles of a rhombus.
4) The sum of two adjacent angles is equal to 180 degrees. (From the above figure, we can say that \[\angle A+\angle B=180{}^\circ \], \[\angle A+\angle C=180{}^\circ \], \[\angle D+\angle C=180{}^\circ \], and \[\angle D+\angle B=180{}^\circ \])
5) Opposite angles are equal. (From the above figure, we can say that \[\angle B=\angle C\] and \[\angle A=\angle D\])
Now, let us suppose if any interior angle (say \[\angle A\]) is given as \[\theta \], then according to the properties of rhombus, we can say that
\[\angle A=\angle D=\theta \], \[\angle B=\angle C\]
And \[\angle A+\angle B=180{}^\circ \].
We can write the equation \[\angle A+\angle B=180{}^\circ \] as
\[\Rightarrow \theta +\angle B=180{}^\circ \]
\[\Rightarrow \angle B=180{}^\circ -\theta =\angle C\]
So, we get that if any of the interior angle of the rhombus is \[\theta \], then other three interior angles will be \[\theta \], \[180{}^\circ -\theta \], and \[180{}^\circ -\theta \].

Note: We should have a better knowledge in the topic of geometry to solve this type of question easily. We should that how to draw a rhombus. We should remember the properties of rhombus. Remember that opposite angles of rhombus are equal. And, also remember that the diagonals of a rhombus bisect each other at right angle that 90 degrees and they bisect the interior angles.