Answer:
The answer is A m<2 = 122 and m<3 = 29
Step-by-step 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
