Answer:
40. a. m∠ABD = 144°
41. a. m∠PLN = 130°
42. a. m∠PLM = 140°
Step-by-step explanation:
40. m∠ABD = 4x
m∠CBD = x
since they are supplementary angles. so:
180 = m∠ABD + m∠CBD
180 = 4x + x
180 = 5x
x = 180/5 = 36
therefore:
m∠ABD = 4x
m∠ABD = 4(36)
m∠ABD = 144°
so. a. m∠ABD = 144°
41. m∠KLP = 3(x-5) +10
m∠MLQ = 2x + 10
since: m∠KLP = m∠MLQ (vertical angles)
so: 3(x-5) +10 = 2x + 10
3x -15 + 10 = 2x +10
3x -5 = 2x + 10
3x - 2x = 10 + 5
x = 15
m∠KLP = 3(x-5) +10
m∠KLP = 3[(15)-5] +10
m∠KLP = 3(10) +10 = 30 + 10
m∠KLP = 40° = m∠MLQ
where: m∠PLN = m∠KLP + 90°
m∠PLN = 40 + 90
m∠PLN = 130°
so: a. m∠PLN = 130°
42. m∠PLO = 4x-30
m∠QLN = 3x-10
where: m∠PLO = m∠QLN (vertical angles)
so: 4x-30 = 3x-10
4x - 3x = 30 - 10
x = 20
m∠PLO = 4x - 30
m∠PLO = 4(20) - 30
m∠PLO = 80-30
m∠PLO = 50°
since: m∠PLM = 90° + m∠PLO
m∠PLM = 90° + 50°
m∠PLM = 140°
so: a. m∠PLM = 140°
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Answers & Comments
Answer:
40. a. m∠ABD = 144°
41. a. m∠PLN = 130°
42. a. m∠PLM = 140°
Step-by-step explanation:
40. m∠ABD = 4x
m∠CBD = x
since they are supplementary angles. so:
180 = m∠ABD + m∠CBD
180 = 4x + x
180 = 5x
x = 180/5 = 36
therefore:
m∠ABD = 4x
m∠ABD = 4(36)
m∠ABD = 144°
so. a. m∠ABD = 144°
41. m∠KLP = 3(x-5) +10
m∠MLQ = 2x + 10
since: m∠KLP = m∠MLQ (vertical angles)
so: 3(x-5) +10 = 2x + 10
3x -15 + 10 = 2x +10
3x -5 = 2x + 10
3x - 2x = 10 + 5
x = 15
m∠KLP = 3(x-5) +10
m∠KLP = 3[(15)-5] +10
m∠KLP = 3(10) +10 = 30 + 10
m∠KLP = 40° = m∠MLQ
where: m∠PLN = m∠KLP + 90°
m∠PLN = 40 + 90
m∠PLN = 130°
so: a. m∠PLN = 130°
42. m∠PLO = 4x-30
m∠QLN = 3x-10
where: m∠PLO = m∠QLN (vertical angles)
so: 4x-30 = 3x-10
4x - 3x = 30 - 10
x = 20
m∠PLO = 4x - 30
m∠PLO = 4(20) - 30
m∠PLO = 80-30
m∠PLO = 50°
since: m∠PLM = 90° + m∠PLO
m∠PLM = 90° + 50°
m∠PLM = 140°
so: a. m∠PLM = 140°