Question

given: ∠12 ≅ ∠7, m∠12 = 65°, m∠8 = 50°. using the diagram in conjunction with postulates and theorems, determine the measures of the unknown angles. 1. <10 is ____ degrees because __ 2. <13 is __ degrees because __ 3. <14 is __ degrees because ____ word bank: corresponding angles theorem, same - side interior angle theorem, alternate interior angle theorem, alternate exterior angle theorem, same - side exterior angle theorem, vertical angle theorem, liner pair postulate

Explanation:

Step1: Identify vertical - angle relationship for ∠10

∠8 and ∠10 are vertical angles. Vertical angles are congruent. Given m∠8 = 50°.
m∠10=m∠8 = 50°

Step2: Identify linear - pair relationship for ∠13

∠12 and ∠13 form a linear pair. The sum of angles in a linear pair is 180°. Given m∠12 = 65°.
m∠13=180° - m∠12=180° - 65° = 115°

Step3: Identify vertical - angle relationship for ∠14

∠13 and ∠14 are vertical angles. Vertical angles are congruent. Since m∠13 = 115°.
m∠14=m∠13 = 115°

Answer:

1. 50, vertical angle theorem
2. 115, liner pair postulate
3. 115, vertical angle theorem