In exercises 5-6, find the measure of angle 1 through 5 in the figure shown

∠1 - 40°

b/c it's a right triangle and we have two angles given, 50° and 90°. Add them and subtract by 180° and get 40°.

∠2 - 140°

b/c an exterior (outside) angle is equal to the two most isolated / farthest angles added. The two most is angles are 105° and 35°, add them and get 140°.

∠3 - 40°

b/c ∠'s 1 and 3 are vertical angles meaning they're equal so since ∠1 is 40°, so is ∠3.

∠4 -

b/c ∠' s 2 and 4 are vertical angles meaning they're equal so since ∠2 is 140°, so is ∠4.

∠5 - 35°

b/c we have two angles, 105° and 40°. Add them and subtract by 180° and get 35°.

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I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

Whenever you see a square in a corner, it means you have a right angle = 90 degrees. A right angle will be on both sides of the line it is next two, since if two crossed lines form a right angle on one side, they also form a right angle on the other side. So, the angle marked 1 is inside a triangle with angles 50 degrees and 90 degrees. The sum of all interior angles in any triangle is 180 degrees. So we have 50 + 90 = 140 degrees so far. That means angle 1 is 180 - 140 = 40 degrees.

Angles 1 and 2 form a line, so they are a linear pair. Linear pair angles are supplementary, meaning they add up to 180 degrees. Since we know m<1 = 40, that means m<2 = 180 - 40 = 140 degrees.

Angles 1 and 3 and angles 2 and 4 are formed by intersecting lines and meet only at their vertices, so they are vertical angle pairs. Vertical angles are congruent, so since m<1 = 40 degrees, m<3 = 40 degrees. Since m<2 = 140 degrees, m<4 = 140 degrees.

For the last triangle, you have angle 3, which we now know is 40 degrees, an angle marked 105 degrees, and angle 5. Since we know the interior angles of any triangle add up to 180 degrees, we have 40 + 105 = 145. And so m<5 = 180 - 145 = 35 degrees.