Answer: Using that the sum of the internal angles of any triangle is equal to 180°, the measurement of angle 4 is 10° (first option).
Step-by-step explanation:
m<3=m<7
m>2=60°
m<6=115°
m<4=x=?
The angles 5 and 6 are adjacent angles, then they must add 180°:
m<5+m<6=180°
Replacing m<6=115° in the equation above:
m<5+115°=180°
Solving for m<5: Subtracting 115° both sides of the equation above:
m<5+115°-115°=180°-115°
Subtracting:
m<5=65°
Using that the sum of the internal angles of any triangle is equal to 180°
m<2+m<3+m<5=180°
Replacing m<2 by 60° and m<5 by 65° in the equation above:
60°+m<3+65°=180°
Adding like terms:
m<3+125°=180°
Solving for m<3: Subtracting 125° both side of the equation above:
m<3+125°-125°=180°-125°
Subtracting:
m<3=55°
m<3=m<7=55°
Using that the sum of the internal angles of any triangle is equal to 180°
m<4+m<6+m<7=180°
Replacing m<6 by 115° and m<7 by 55° in the equation above:
m<4+115°+55°=180°
Adding like terms:
m<4+170°=180°
Solving for m<4: Subtracting 170° both side of the equation above:
m<4+170°-170°=180°-170°
Subtracting:
m<4=10°
