Question

1) LaTeX: m\angle1=\:\:\:\:\:\:\:\:^\circm ∠ 1 = ∘

2) LaTeX: m\angle2=\:\:\:\:\:^\circm ∠ 2 = ∘

3) LaTeX: x\:=\:\:\:\:m\:\left(exterior\:angle\right)\:=

Answer 1

1. m<1 = 139°

2. m<2 = 41°

3. x = 29

Explanation:

1. m<1 = 86° + 53° (exterior angle theorem of a triangle)

m<1 = 139°

2. 133° = m<2 + 92° (exterior angle theorem of a triangle)

133° - 92° = m<2 (Subtraction property of equality)

41° = m<2

m<2 = 41°

3. 4x + 15 = 93° + (x + 9)° (exterior angle theorem of a triangle)

Add like terms

4x + 15 = 102 + x

4x - x + 15 = 102 (substraction property of equality)

3x + 15 = 102

3x = 102 - 15

3x = 87

x = 87/3 (division property of equality)

x = 29