Please help! I’m this figure, which angles are congruent? Find the measure of all the angles if m< 2= 76 degrees

Problem 1.

Yes it is true that vertical angles are congruent, but that's not what your teacher is asking. Instead, your teacher is asking basically how the term "congruent" is defined.

Two segments are congruent if they are the same length. Two angles are congruent if they are the same measure. Two triangles are congruent if they have the same angles and sides.

So in short, "congruent" just means "same". You can think of having mirror copies.

Problem 2.

Angles 2 and 4 are one pair of vertical angles. They are opposite one another in this X shape formed by the two lines. The other pair of vertical angles are angle 1 and angle 3.

Angle 2 is given to be 76 degrees, so this means angle 4 is this measure as well.

Angle 1 = 180 - (angle 2) = 180 - 76 = 104, which is also the measure of angle 3 as well. I'm using the idea that the adjacent angles form a straight angle. This is known as a linear pair (ie the angles form a straight line).

Problem 3.

If all three angles are the same (all 60 degrees), then we have an equilateral triangle. We could say it's equiangular, but it's also equilateral as well meaning all 3 sides are the same length. "equi" means "equal", "angular" means what you'd expect, and "lateral" means "side".

If only two angles are equal with the third one different, then we have an isosceles triangle. An isosceles triangle is one where only two sides are the same length.

If none of the angles are the same, then we have a scalene triangle. As you probably expect, none of the sides are the same length with a scalene triangle.

If all three angles are less than 90 degrees, then the triangle is acute

If one angle is 90 degrees, then we have a right triangle

If one angle is over 90 degrees (but less than 180), then the triangle is obtuse

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Often you'll see the terms of the previous two sections combined. For instance, we could have an isosceles right triangle. Or we might have an obtuse scalene triangle. Any equilateral triangle is acute (as all three angles are less than 90).

the answer is 844

step-by-step explanation:

it is 844 because if you add 836.50 + 7.5 you will get 844