Drag each angle measure to the correct location on the image. Not all angle measures will be used.
Determine the measures of the angles.
35°
70°
75°
100°
105°
110°

Given:

One internal angle = 75°

External angle = 145°

To find:

The measure of each angle.

Solution:

The reference image is attached below.

The measure of exterior angle is equal to the sum of the measures of the opposite interior angles.

⇒ m∠A + m∠B = ext ∠C

⇒ m∠A + 75° = 145°

Subtract 75° from both sides.

⇒ m∠A + 75° - 75° = 145° - 75°

⇒ m∠A = 70°

Sum of all the angles of a triangle = 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 70° + 75° + m∠C = 180°

⇒ 145° + m∠C = 180°

Subtract 145° from both sides.

⇒ 145° + m∠C - 145° = 180° - 145°

⇒ m∠C = 35°

By external angle theorem,

ext∠B = m∠A + m∠C

          = 70° + 35°

ext∠B = 105°

By external angle theorem,

ext∠A = m∠B + m∠C

          = 75° + 35°

ext∠B = 110°

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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