Question

select the correct answer. in the figure, angle c measures 83°, angle f measures 105°, and angle e measures 37°. what is the measurement of angle i? a. 37° b. 45° c. 51° d. 76°

Explanation:

Step1: Find angle in triangle with ∠C and ∠E

Sum of angles in a triangle is 180°. Let the third - angle in triangle with ∠C and ∠E be ∠x. So, ∠x=180°−(83° + 37°)=60°.

Step2: Use linear - pair and angle - sum property

∠x and an angle adjacent to it in the other triangle form a linear pair. So, the adjacent angle is 180° - 60° = 120°. In the triangle with ∠F and this adjacent angle, let the third - angle be ∠I. Then ∠I=180°−(120° + 105°)=51°.

Answer:

C. 51°