Question

ABCD is a rhombus. If m<1=122, then what is the measure of <2 and <3

Answer 1

The answer is A.

Angles 1 and 2 are congruent, therefore angle 2 = 122.

The sum of all three angles in a single triangle would be 180.

180 - 122 = 58

Therefore, each of the other angles have to be LESS than 58.

Answer 2

The answer is A m<2 = 122 and m<3 = 29

Explanation:

There are several ways to solve the problem. using these theorems:

a) Opposite internal angles of a rhombus are congruent.

<1 is opposite to <2 so they must be congruent. Then if <1 measures 122, < 2 also measures 122

Also angle A and angle C are congruent so <A = <C

b) Internal angles of a rhombus ( a type of quadrilateral - 4 sides ) sum 360 degrees.

Then if this is true

<1 +<2+<A+<C = 360

but <A=<C because of a) so

<1+<2+<C+<C = 1+<2+ 2(<C) = 360 Then we replace the values of <1 and < 2 that we know

122+122 + 2(<C) = 360

244+ 2(<C) = 360

2(<C) = 360-244 = 116

<C=116/2 = 56

Now this is the measure of < C but we need angle 3. So we can finally use the fact that:

b) A diagonal of a rhombus bisects an angle into two congruent separate angles.

The diagonal breaks <C in two congruent angles one which is <3 so

<3 = <C/2 =56 /2 = 29

The answer is A m<2 = 122 and m<3 = 29