In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation. Angle Pairs Definitions
Example Finding an Angle Measure ∠1 and ∠2 are complementary, and m∠2 = 32 . Find m∠1.Solution
Are ∠1 and ∠2 are complementary, supplementary, or neither? 1. m∠1 = 79 m∠2 = 101 2. m∠1 = 53 m∠2 = 47
m∠2 = 85 4. m∠2 = 38
When two lines intersect at a point, they form two pairs of angles that do not share a side. These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.
Example Find m∠2, m∠3, and m∠4. Solution ∠1 and ∠3 are vertical angles. Their measures are equal, so m∠3 = 90. ∠1 and ∠2 are supplementary.
90 + m∠2 = 180 Substitute 90 for m∠1. m∠2 = 90 Subtract 90 from each side.
ANSWER: m∠2 = m∠3 = m∠4 = 90 Perpendicular Lines When two lines intersect to form one right angle, they form four right angles. Two lines that intersect at a right angle are called perpendicular lines. Practice Find the measures of the numbered angles. 5. 6.
Parallel Lines Two lines in the same plane that do not intersect are called parallel lines. When a line intersects two parallel lines, several pairs of angles that are formed have equal measures. Angles and Parallel Lines Example Corresponding Angles: m∠1 = m∠5; m∠2 = m∠6; Alternate Interior Angles: m∠3 = m∠6; m∠4 = m∠5 Alternate Exterior Angles: m∠1 = m∠8; m∠2 = m∠7 Using Parallel Lines
Use the diagram to find m∠1.
Find m∠5. The angle with measure 125 and ∠5 are supplementary.
m∠5 = 55 Subtract 125 from each side.
Find the angle measure.
7. m∠2
9. m∠4 10. m∠6
12. Two lines that intersect to form a right angle are called _?_.
13. m∠1 = 62 , m∠2 = 11814. m∠1 = 51 , m∠2 = 39
15.
m∠2 = 68 , because vertical angles add up to 180.
16. m∠1= (5x + 15) and m∠2 = 28x
19. A student designed the stationery border shown here. Explain how to find m∠2 if m∠1 = 135 .Answers 1. supplementary 2. neither 3. supplementary 4. complementary 5. m∠9 = 126o; m∠10 = 54o; m∠11 = 126o 6. m∠6 = 43o; m∠7 = 137o; m∠8 = 43o 7. 85o 8. 95o 9. 85o 10. 85o 11. supplementary 12. perpendicular 13. supplementary 14. complementary 15. Vertical angles are congruent, so m∠2 = 112o. 16. 5 17. 13 18. m∠2 = 58o; m∠3 = 122o; m∠4 = 58o 19. Angles 1 and 2 form a linear pair and are supplementary. So to find m∠2, subtract m∠1 from 180o. m∠2 = 180o - 135o = 45o. |