Question

find the angle measure x in the following figures​

Answer 1

Answer:

let first give naming to the figure

It is given the TQR is a straight line and so, the linear pairs (i.e. TQP and PQR) will add up to 180°

So, TQP +PQR = 180°

Now, putting the value of TQP = 110° we get,

PQR = 70°

Consider the ΔPQR,

Here, the side QP is extended to S and so, SPR forms the exterior angle.

Thus, SPR (SPR = 135°) is equal to the sum of interior opposite angles. (Triangle property)

Or, PQR +PRQ = 135°

Now, putting the value of PQR = 70° we get,

PRQ = 135°-70°

Hence, PRQ = 65°

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Answer 2

Answer:

$\boxed{Mark \: me \: as \: a \: Brainliest \: pls }$

Step-by-step explanation:

We know that the sum of the exterior angles of a triangle is 360°

So,

135° + 115° + ∠x = 360°

=> ∠x = 360° - 250°

$\Rightarrow\boxed{ ∠x = 110°}$

or by using Linear pair find all the interior angles of the triangle and then using angle sum property of triangle nad linear pair find the ∠x we get the same answer