Question

Can help anyone answer this?

Answer 1

Answer: D) 120 degrees

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Step-by-step explanation:

Let y be the measure of the interior angle adjacent to the 130 degree exterior angle

y+130 = 180

y = 180-130

y = 50

Interior angle D is 50 degrees.

It adds to angle C getting 50+70 = 120, which is the measure of angle 1 due to the remote interior angle theorem.

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We can see it if we let angle 2 be x

B+C+D = 180 ... interior angles of a triangle add to 180

x+70+50 = 180

x+120 = 180

x = 180-120

x = 60

angle B = 60

To find angle 1, we subtract this from 180, since

(angle1)+(angle2) = 180

(angle1)+(60) = 180

angle1 = 180-60

angle1 = 120

This leads to the same result as before.

Answer 2

`\huge\boxed{\text{(D)} \ 120 \textdegree}`

Step-by-step explanation:

We can use basic angle relationships to find m∠1.

We know that the 130° angle and m∠D are supplementary. This means their angle measures add up to 180°. Since we know one, we can find m∠D by subtracting it from 180.

`180-130=50`

So m∠D is 50°.

We also know that all angles in a triangle add up to 180°. Since we know two out of the three, we can add the two and subtract from 180.

`70+50=120\\\\180-120=60`

So m∠2 = 60°.

Again, m∠2 and m∠1 are supplementary. Since we know 1, we can find m∠1 by subtracting from 180.

`180-60=120`

So m∠1 is 120°.

Hope this helped!