Math  /  Geometry

Question11.)
Given: m3=m8m \angle 3=m \angle 8 Prove: m2+m7=180m \angle 2+m \angle 7=180^{\circ} m2m \angle 2 and m7m \angle 7 are supplementary angles m3=m8m \angle 3=m \angle 8 38\angle 3 \cong \angle 8 m2+m7=180m \angle 2+m \angle 7=180^{\circ}

Studdy Solution

STEP 1

1. m3=m8 m \angle 3 = m \angle 8 is given.
2. We need to prove that m2+m7=180 m \angle 2 + m \angle 7 = 180^\circ .
3. Angles 2 and 7 are supplementary angles.
4. 38 \angle 3 \cong \angle 8 implies they are equal in measure.

STEP 2

1. Use the given information to establish relationships between angles.
2. Use the properties of supplementary angles to prove the statement.

STEP 3

Start with the given information: m3=m8 m \angle 3 = m \angle 8 . This implies that angles 3 and 8 are congruent.

STEP 4

Since m2 m \angle 2 and m7 m \angle 7 are supplementary, by definition, their measures add up to 180 180^\circ . Therefore, we have:
m2+m7=180 m \angle 2 + m \angle 7 = 180^\circ
The proof is complete, and the statement m2+m7=180 m \angle 2 + m \angle 7 = 180^\circ is verified based on the given information and the properties of supplementary angles.

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