Question

in the given figure if PQ parallel to rs then find the measure of angle m​

Answer 1

Answer:

Given

PQ∥RS

∠QRS=∠PSR(alternateangles)= 56o  

By angle sum property  

14o + 56o + m=180o

m=110o

Step-by-step explanation:

Answer 2

Given: The figure is given where PQ is parallel to RS.

To find: The measure of the angle m.

Solution:

In the given figure, PQ is parallel to RS, therefore;

∠QPS = ∠TSR  (∵Because they are alternate angles and by the property of parallel angles we know alternate angles are equal.)

Now, In ΔTSR

∠TRS = $14^o$

∠TSR = ∠QPS = $56^o$

By the property of triangles, we know that the sum of all the angles in a triangle is $180^o$

∴ ∠TSR + ∠TRS + ∠STR = $180^o$

⇒ $56 + 14 + m = 180$

⇒ $70+m=180$

⇒ $m= 180-70$

⇒ $m = 110^o$

Final answer:

Hence the measure of angle m is $110^o$.