in the rhombus, m<1=160. what are m<2 and m<3? Can someone explain this to me??
To determine the measures of angles 2 and 3 in a rhombus when angle 1 is given, we can use the properties of a rhombus.
First, let's understand the properties of a rhombus:
1. All sides of a rhombus are equal in length.
2. Opposite angles in a rhombus are congruent.
3. The diagonals of a rhombus bisect each other at right angles.
In a rhombus, angle 1 and angle 2 are opposite angles, as are angle 3 and angle 4. Similarly, angle 2 and angle 4, as well as angle 1 and angle 3, are adjacent angles.
Given that angle 1 is 160 degrees, we can conclude that:
1. Angle 1 = Angle 2 since they are opposite angles.
2. Angle 1 + Angle 3 = 180 degrees (since the sum of adjacent angles is 180 degrees).
Therefore:
1. Angle 2 = Angle 1 = 160 degrees.
2. Angle 3 = 180 degrees - Angle 1 = 180 degrees - 160 degrees = 20 degrees.
So, Angle 2 is 160 degrees, and Angle 3 is 20 degrees.
To find the measures of angles 2 and 3 in a rhombus, let's consider the properties of a rhombus.
In a rhombus, opposite angles are congruent. Since angle 1 measures 160 degrees, angle 3, which is opposite angle 1, also measures 160 degrees.
Therefore, m<3 = 160 degrees.
To find the measure of angle 2, we'll use another property of a rhombus: the sum of all angles in a rhombus is 360 degrees.
Since angle 1 measures 160 degrees and angle 3 measures 160 degrees, the remaining two angles (angles 2 and 4) must add up to 360 - 160 - 160 = 40 degrees.
Since a rhombus has congruent opposite angles, angle 2 and angle 4 are congruent. Therefore, each of these angles measures half of the remaining sum: 40 degrees / 2 = 20 degrees.
Therefore, m<2 = m<4 = 20 degrees.
In a rhombus, opposite angles are equal, each 160° ,
leaving 20° for the other opposite angle pair.