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1-4 Angles

1-4 Angles. o. ALGEBRA Given that m LKN =145 , find m LKM and m MKN . STEP 1. Write and solve an equation to find the value of x. m LKN = m LKM + m MKN. o. o. o. 145 = (2 x + 10) + (4 x – 3). EXAMPLE 3. Find angle measures. SOLUTION. Angle Addition Postulate.

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1-4 Angles

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  1. 1-4 Angles

  2. o ALGEBRAGiven that m LKN =145 , find m LKM andm MKN. STEP 1 Write and solve an equation to find the value of x. mLKN = m LKM + mMKN o o o 145 = (2x + 10)+ (4x – 3) EXAMPLE 3 Find angle measures SOLUTION Angle Addition Postulate Substitute angle measures. 145 = 6x + 7 Combine like terms. 138 = 6x Subtract 7 from each side. 23 = x Divide each side by 6.

  3. STEP 2 Evaluate the given expressions when x = 23. mLKM = (2x+ 10)° = (2 23+ 10)° = 56° mMKN = (4x– 3)° = (4 23– 3)° = 89° So, m LKM = 56°and m MKN = 89°. ANSWER EXAMPLE 3 Find angle measures

  4. 3. Given that KLMis straight angle, find mKLN andm NLM. STEP 1 Write and solve an equation to find the value of x. m KLM + m NLM = 180° (10x – 5)° + (4x +3)° = 180° = 180 14x – 2 = 182 14x x = 13 for Example 3 GUIDED PRACTICE Find the indicated angle measures. SOLUTION Straight angle Substitute angle measures. Combine like terms. Subtract 2 from each side. Divide each side by 14.

  5. STEP 2 Evaluate the given expressions when x = 13. mKLM = (10x– 5)° = (10 13– 5)° = 125° mNLM = (4x+ 3)° = (4 13+ 3)° = 55° mKLM = 125° mNLM = 55° ANSWER for Example 3 GUIDED PRACTICE

  6. STEP 1 Write and solve an equation to find the value of x. m EFG + m HFG m EFG EFG is a right angle = = 90° (2x + 2)° + (x +1)° = 90° = 90 3x + 3 = 87 3x x = 29 for Example 3 GUIDED PRACTICE 4. Given that EFGis a right angle, find mEFH andm HFG. SOLUTION Substitute angle measures. Combine like terms. Subtract 3 from each side. Divide each side by 3.

  7. STEP 2 Evaluate the given expressions when x = 29. mEFH = (2x+ 2)° = (2 29 +2)° = 60° mHFG = (x+ 1)° = (29+ 1)° = 30° mEFG = 60° mHFG = 30° ANSWER for Example 3 GUIDED PRACTICE

  8. The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m DEG = 157° ,what is m GKL? SOLUTION There are two pairs of congruent angles: DEF JKL and DEG GKL. Because ∠ DEG GKL, DEG = mGKL. So, mGKL = 157°. ~ ~ ~ EXAMPLE 4 Identify congruent angles Trapeze

  9. Use the diagram shown below. ~ ~ T S andPQ. for Example 4 GUIDED PRACTICE 5. Identify all pairs of congruent angles in the diagram. SOLUTION There are two pairs of Congruent angles in the diagram.

  10. Use the diagram shown at the right. o o 6. In the diagram, mPQR = 130 , mQRS = 84, and m TSR = 121 . Find the other angle measures in the diagram. o PTS TSR = 121° = 84° ~ ~ QRS QPT for Example 4 GUIDED PRACTICE SOLUTION Congruent angles Congruent angles

  11. In the diagram at the right, YWbisects XYZ, and mXYW = 18. Find m XYZ. o By the Angle Addition Postulate, m XYZ =mXYW + m WYZ. BecauseYW bisects XYZyou know thatXYW WYZ. So, m XYW = m WYZ, and you can write M XYZ = m XYW + m WYZ = 18° + 18° = 36°. ~ EXAMPLE 5 Double an angle measure SOLUTION

  12. 7. Angle MNPis a straight angle, and NQbisects MNP. Draw MNP And NQ. Use arcs to mark the congruent angles in your diagram, and give the angle measures of these congruent angles. SOLUTION for Example 5 GUIDED PRACTICE

  13. 2 m MNQ = 180° = 90° m MNQ = mPNQ m MNQ + mPNQ m MNQ + mPNQ = 180° = 180° The solution is = 90° m MNQ = mPNQ m MNQ + mMNQ m MNQ for Example 5 GUIDED PRACTICE Angle addition postulate Straight angle Add Divided each side by 2

  14. Name the three angles in the diagram. WXY, or YXW YXZ, or ZXY WXZ, or ZXW You should not name any of these angles X because all three angles have Xas their vertex. EXAMPLE 1 Name angles

  15. Use the diagram to find the measure of the indicated angle. Then classify the angle. a.KHJ b. GHK c. GHJ d. GHL EXAMPLE 2 Measure and classify angles SOLUTION A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.

  16. o a.HJ is lined up with the 0 on the inner scale of the protractor. HKpasses through 55 on the inner scale. So, mKHJ = 55 . It is an acute angle. o o o b.HG is lined up with the 0 on the outer scale and HKpasses through 125 on the outer scale. So,mGHK = 125 . It is an obtuse angle. o o o c.m GHJ = 180. It is a straight angle. o d.m GHL= 90. It is a right angle. EXAMPLE 2 Measure and classify angles

  17. ANSWER PQR , PQS, RQS . PQS is a right angle . for Examples 1and 2 GUIDED PRACTICE 1. Name all the angles in the diagram at the right.Which angle is a right angle?

  18. Straight Angle ANSWER for Examples 1and 2 GUIDED PRACTICE 2. Draw a pair of opposite rays. What type of angle do the rays form?

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