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< TRS and <SRP form a linear pair. If m<TRS

= 3a + 5 and m<SRP =2a - 25, find m<TRS.​

1 Answer

6 votes

Explanation:

linear pair of angles are formed at the intersection point of two lines.

the 2 angles are a linear pair, if they are adjacent (next) to each other at the intersection point. that way they cover together a whole side of one of the lines.

the sum of a linear pair is therefore always equal to 180°. a linear pair of angles is also known as supplementary angles (together they represent 180°).

so, bottom line, together they are 180°.

that means

(3a + 5) + (2a - 25) = 180

that we can solve for a :

3a + 5 + 2a - 25 = 180

5a - 20 = 180

5a = 200

a = 200/5 = 40

angle TRS = 3a + 5 = 3×40 + 5 = 120 + 5 = 125°

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