Question

Given that m<2=3x - 11 and m<5 = 7x + 46 use the figure to answer question 1-3

Answer 1

Applying the relationship of angle pairs, THE VALUE OF X AND THE GIVEN ANGLE MEASURES ARE:

• x = 14.5 (Blue)
• m<5 = 147.5 degrees (Yellow)
• m<4 = 32.5 degrees (Pink)

Given:

m<2 = 3x - 11

m<5 = 7x + 46

Thus, find x:

<2 and <5 are same-side interior angles

• Therefore:

m<2 + m<5 = 180 degrees (supplementary)

• Substitute

$3x - 11 + 7x + 46 = 180$

• Collect like terms

$10x +35 = 180\\\\10x = 180 - 35\\\\10x = 145\\\\\mathbf{x = 14.5}$(Blue)

Find m<5:

Plug in the value of x into 7x + 46

$m \angle 5 = 7(14.5) + 46\\\\\mathbf{m \angle 5 = 147.5^{\circ}}$(Yellow)

Find <4:

m<4 = m<2 (vertical angles are congruent)

• Substitute

m<4 = 3x - 11

• Plug in the value of x

m<4 = 3(14.5) - 11

m<4 = 32.5 degrees (Pink)

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