Find all angles and pls show steps

Mathematics

1 answer:

Ghella [55]2 years ago

7 0

Answer:

Both angles have a measure of 134degrees, y = 27degrees.

Step-by-step explanation:

As per what is given in the problem:

There are 2 parallel lines, both are intersected by a transversal.

Remember the theorem, when two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent.

The is meanse that:

3y + 53 = 7y - 55

Solve using inverse operations:

3y + 53 = 7y - 55

+55 +55

3y + 108 = 7y

-3y -3y

108 = 4y

/4 /4

27 = y

Now, substitute back in to find the value of the angle:

3y + 53

y = 27

3 ( 27 ) + 53

81 + 53

= 134

Since the angles are alternate exterior, they are congruent, hence both angles have a measure of 134degrees.

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dexar [7]

The sum of the measures of two complementary angles is 90°. To put it another way, m∠P + m∠Q = 90°.

So, we can substitute the given values of the angles into this equation.

$(52)+(3x+2)=90 \\ \\ 3x+54=90 \\ \\ 3x=36 \\ \\ x=12$

Then, to find m∠Q, we plug in 12 for x for the original expression of Q to get $3(12)+2=38$ .