Question

3. In the rhombus, what are m∠1, m∠2 and m∠3? The diagram is not drawn to scale.

Answer 1

Answer: m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.

Step-by-step explanation:  We are given to find the measures of ∠1, ∠2 and ∠3 in the figure.

As shown in the attached figure, ABCD is a rhombus, where m∠A = 128°.

We know that, in a rhombus, all the sides are congruent,  the opposite angles are congruent and the adjacent angles are supplementary.

So, from rhombus ABCD, we have

$m\angle A=m\angle C~~~~~\textup{[opposite angles]}\\\\\Rightarrow m\angle 1=128^\circ.$

Also, in ΔBCD, we have

$BC=CD~~\textup{[all the sides are congruent]}\\\\\Rightarrow m\angle 3=m\angle 2~~\textup{[angles opposite to congruent sides care congruent]}.$

Now, since the sum of three angles of a triangle is 180°, we have from  ΔBCD that

$m\angle 1+m\angle 2+m\angle 3=180^\circ\\\\\Rightarrow 128^\circ+m\angle 2+m\angle 2=180^\circ\\\\\Rightarrow 2\times m\angle 2=180^\circ-128^\circ\\\\\Rightarrow 2\times m\angle 2=52^\circ\\\\\Rightarrow m\angle 2=26^\circ.$

Therefore, m∠3 = 26°.

Thus, m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.

Answer 2

M< 1 = 128, m< 2 = 26, and m< 3 = 26.