Our transversal and parallel lines create four pairs of corresponding angles. When the corresponding angles are on parallel lines, they are congruent. Angles that have the same position relative to one another in the two sets of four angles (four at the top, Line AR four at the bottom, Line TO) are corresponding angles. We can adroitly pull from this figure angles that look like each other. When a line crosses two parallel lines (a transversal), a whole new level of angle relationships opens up: Angle relationships - corresponding angles The more restrictive our intersecting lines get, the more restrictive are their angle relationships. Corresponding anglesĪnytime a transversal crosses two other lines, we get corresponding angles. Adjacent angles share more than the vertex they share a common side to an angle. You may wonder why adjacent angles are not also vertical angles, since they share the vertex, too. See if you can spot them in our drawing.ĭid you find ∠JYO and ∠KYC made a pair? They touch only at Point Yĭid you find ∠KYJ and ∠OYC made the other pair? They also touch only at Point Y Two intersecting lines create two pairs of vertical angles. Here the word 'vertical' means 'relating to a vertex,' not 'up and down.' Vertical angles are opposite angles they share only their vertex point. In our same drawing above, angles that skip an angle, that is, angles that are not touching each other except at their vertex, are vertical angles. Can you find them all? Angle relationships - adjacent anglesĪnd you found ∠KYJ adjacent to ∠JYO, surely! In the following drawing, Line JC intersects Line OK, creating four adjacent pairs and intersecting at Point Y. Any two angles sharing a ray, line segment or line are adjacent. When two lines cross each other, they form four angles. So these two 35° angles are congruent, even if they are not identically presented, and are formed with different constructions: Angle relationships - congruent angles Adjacent angles They show the same 'openness' between the two rays, line segments or lines that form them. Congruent anglesĪny two angles, no matter their orientation, that have equal measures (in radians or degrees) are congruent. You will solve complex problems faster when you are thoroughly familiar with all the types of angle relationships. When two parallel lines are intersected by a transversal, complex angle relationships form, such as alternating interior angles, corresponding angles, and so on.īeing able to spot angle relationships, and confidently find congruent angles when lines intersect, will make you a better, geometry student. Types of angles - angle relationshipsįor example, when two lines or line segments intersect, they form two pairs of vertical angles. We talk of angle relationships because we are comparing position, measurement, and congruence between two or more angles. An angle measuring 15° is an acute angle.Beyond measuring the degrees or radians, you can also compare angles and consider their relationships to other angles.An angle measuring 90° is an obtuse angle.An angle measuring 85° is an acute angle.An angle measuring 45° is a right angle.Question 2: Measure of some angles are given below: ∠AĪnswer: The acute angles are: ∠A, ∠B, and ∠E as all these angles are less than 90° Acute angle- since 17° is less than 90°.Obtuse angle- since 112° is more than 90°.Acute angle- since 75° is less than 90°.Question 1: The measure of three angles is as follows: In a 180˚angle, if one angle is obtuse (more than 90˚), the other will always be an acute angle (less than 90˚). At least two angles of any triangle are acute angles.Ģ. For example, in an equilateral triangle, all three angles measure 60˚, making it an acute triangle.ġ. Acute TriangleĪ triangle formed by all angles measuring less than 90˚ is also known as an acute triangle. The hour hand and the minute hand form an acute angle at 10 o’clock.Ī pair of open scissors, alligator’s open mouth, and the beak of birds all form acute angles. The arms of a wall clock make acute angles at several hours of the day. If we slice a pizza into 5 or more slices, each slice of pizza will make an acute angle.Įach slice of the pizza makes an acute angle.Īnother example is the wall clock. Right Angle Two acute angles are formed byĭividing the right angle. Therefore, 67°, 45°, 23°, 52°, 86°, 14° are all examples of acute angles.ĭividing the right angle (90˚) will give us two or more acute angles since each newly formed angle will be less than 90˚. ∠ABC measures 30° and hence it is an acute angle. Any angle that measures greater than 0° and less than 90° is called an acute angle.

Whats a supplementary angle