Question

Can someone please help with this!

Answer 1

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