Adjacent angles: two angles with a common vertex, sharing a common side and no overlap. Show Complementary angles: two angles, the sum of whose measures is 90°. Angles ∠1 and ∠2 are complementary. Complementary are these angles too(their sum is 90°): Supplementary angles: two angles, the sum of whose measures is 180°. Angles ∠1 and ∠2 are supplementary. When two parallel lines are given in a figure, there are
two main areas: the interior and the exterior. When two parallel lines are cut by a third line, the third line is called the transversal. In the example below, eight angles are formed when parallel lines m and n are cut by a transversal line, t. There are several special pairs of angles formed from this figure. Some pairs
have already been reviewed: Alternate interior angles two angles in the interior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate interior angles are non-adjacent and congruent. Alternate exterior angles two
angles in the exterior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate exterior angles are non-adjacent and congruent. Corresponding angles two angles, one in the interior and one in the exterior, that are on the same side of the transversal. Corresponding angles are non-adjacent and congruent. Use the following diagram of parallel lines cut by a transversal to answer the example problems. Example: What is the measure of ∠8? The angle marked with measure 53° and ∠8 are alternate exterior angles. They are in the exterior, on opposite sides of the transversal. Because they are congruent, the measure of ∠8 = 53°. Example: What is the measure of ∠7? ∠8 and ∠7 are a linear pair; they are supplementary. Their measures add up to 180°. Therefore, ∠7 = 180° – 53° = 127°. 1. When a transversal cuts parallel lines, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent. In the figure above ∠1, ∠4, ∠5, and ∠7 are all acute angles. They are all congruent to each other. ∠1 ≅ ∠4 are vertical angles. ∠4 ≅ ∠5 are alternate interior angles, and ∠5 ≅ ∠7 are vertical angles. The same reasoning applies to the obtuse angles in the figure: ∠2, ∠3, ∠6, and ∠8 are all congruent to each other. 2. When parallel lines are cut by a transversal line, any one acute angle formed and any one obtuse angle formed are supplementary. From the figure, you can see that ∠3 and ∠4 are supplementary because they are a linear pair. Notice also that ∠3 ≅ ∠7, since they are corresponding angles. Therefore, you can substitute ∠7 for ∠3 and know that ∠7 and ∠4 are supplementary. Example: The angle supplementary to ∠1 is ∠6. ∠1 is an obtuse angle, and any one acute angle, paired with any obtuse angle are supplementary angles. This is the only angle marked that is acute. Other resources: Angles - Problems with Solutions What type of angle pair is 3 and 5?When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles. In the figure, the angles 3 and 5 are consecutive interior angles.
What type of angle pair is 6 and 4?6 and 4 are alternate exterior angles and thus congruent which means angle 4 is 65°.
What is angle 4 and angle 6 called?For example, ∠4 and ∠6 are corresponding angles, therefore they are congruent.
What type of angle pair is 3 and 4?Supplementary angles are two angles whose measures have a sum of 180°. Angles 3 and 4 are supplementary angles. Complementary angles are two angles whose measures have a sum of 90°.
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