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Inga [223]
2 years ago
10

(100 POINTS) lol help me plz

Mathematics
1 answer:
pishuonlain [190]2 years ago
7 0

Since <em>l</em> and <em>m</em> are parallel, the unlabeled angle adjacent to the 63° one also has measure (7<em>x</em> - 31)° (it's a pair of alternating interior angles).

Then the three angles nearest line <em>m</em> are supplementary so that

(7<em>x</em> - 31)° + 63° + (5<em>x</em> - 8)° = 180°

Solve for <em>x</em> :

(7<em>x</em> - 31) + 63 + (5<em>x</em> - 8) = 180

12<em>x</em> + 24 = 180

12<em>x</em> = 156

<em>x</em> = 13

The bottom-most angle labeled with measure (4<em>y</em> + 27)° is supplementary to the angle directly adjacent to it, so this unlabeled angle has measure 180° - (4<em>y</em> + 27)° = (153 - 4<em>y</em>)°. The interior angles of any triangle have measures that sum to 180°, so we have

(7<em>x</em> - 31)° + 63° + (153 - 4<em>y</em>)° = 180°

We know that <em>x</em> = 13, so 7<em>x</em> - 31 = 60. Then this simplifies to

123° + (153 - 4<em>y</em>)° = 180°

Solve for <em>y</em> :

123 + (153 - 4<em>y</em>) = 180

276 - 4<em>y</em> = 180

96 = 4<em>y</em>

<em>y</em> = 24

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