Given the following diagram, find the required measure. given: m 3 = m 7m 2 = 60°m 6 = 115°m 4 =10 202530

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°

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