Answer:
m<1 = 100 (C)
m<2 = 50 (B)
Step-by-step explanation:
The triangle with two 50degree angles is triangle1, the other triangle (with a 60degree angle) is triangle2.
Let us also call the third angle in triangle1, <x, and the verticle angle to x (when two lines intersect, 4 angles are formed, the angles opposite each other are verticle angles, and they are congruent (the same measure)), <y.
The sum of measures of angles in a triangle is 180 degrees,
using this we can say:
50 + 50 + m<x = 180
simplify
100 + m<x = 180
inverse operations
100 + m<x = 180
-100 -100
m<x = 80
Remember, a straight angle has 180degrees in measure.
As per the picture, <x and <1 add up to form a straight angle.
Using this, form an equation:
m<x + m<1 = 180
substitute
80 + m<1 = 180
inverse operations
80 + m<1 = 180
-80 -80
m<1 = 100
Remember what was said earlier about verticle angles being congruent. This means that m<x = m<y = 80. This can be used to an advantage when setting up an equation:
50 + m<y + m<2 = 180
substitute
50 + 80 + m<2 = 180
simplify
130 + m<2 = 180
inverse operations
130 + m<2 = 180
-130 -130
m<2 = 50
