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 $$\mathrm{\angle }A+\mathrm{\angle }B=180{}^{\circ }$$, $$\mathrm{\angle }A+\mathrm{\angle }C=180{}^{\circ }$$, $$\mathrm{\angle }D+\mathrm{\angle }C=180{}^{\circ }$$, and $$\mathrm{\angle }D+\mathrm{\angle }B=180{}^{\circ }$$)
5) Opposite angles are equal. (From the above figure, we can say that $$\mathrm{\angle }B=\mathrm{\angle }C$$ and $$\mathrm{\angle }A=\mathrm{\angle }D$$)
Now, let us suppose if any interior angle (say $$\mathrm{\angle }A$$) is given as $$\theta$$, then according to the properties of rhombus, we can say that
$$\mathrm{\angle }A=\mathrm{\angle }D=\theta$$, $$\mathrm{\angle }B=\mathrm{\angle }C$$
And $$\mathrm{\angle }A+\mathrm{\angle }B=180{}^{\circ }$$.
We can write the equation $$\mathrm{\angle }A+\mathrm{\angle }B=180{}^{\circ }$$ as
$$\Rightarrow \theta +\mathrm{\angle }B=180{}^{\circ }$$
$$\Rightarrow \mathrm{\angle }B=180{}^{\circ }-\theta =\mathrm{\angle }C$$
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.