Question

In the given figure, TU ll SR and TR ll SV, then find angle a and angle b.

Answer 1

Answer:

a=115, B=40.

Step-by-step explanation:

TU||SR and TR is a transversal line

TRS+RTU=180

TRS=90

PRQ=90(V.O.A)

In PRQ

P+Q+R=180

50+b+90=180

b=40

TR||SV

RTU+UVS=90+25=115

a=115

Answer 2

Answer:

The value of a is 115° and b is 40°.

CONCEPT:

• When a line is transversal and cuts two parallel lines , then each pair of internal angles on the same side of transversal is supplementary (180°)
• Angle opposite to a same vertex are equal.
• The sum of all the three angles in a triangle is always 180°.

GIVEN:

1. TU||SR
2. TR||SV

TO FIND:  the value of ∠a and ∠b

SOLUTION:

By considering only line UT , SR and TR; line TR act as transversal as it is given to us that SR is parallel to the line UT.

So,

∠UTR + ∠TRS = 180

From the given figure , it is already given ∠UTR as 90° . Putting it in the above equation, we get

∠TRS = 90°

As R act as common vertex,

∠TRS = ∠PRQ= 90°

Now in the triangle PQR.

∠RPQ+∠PRQ+∠RQP=180°

From the figure given to us , we can see the value of ∠RPQ is 50°. Putting the values in above equation, we get

$50+90+$∠RQP $=180$

∠RQP = $180-50-90$

∠RQP =$180-140$

∠RQP =40°=b

Hence the value of b is 40°.

Now it is also given to that the line TR is parallel to the line SV.

SO,

∠TRU+∠UVS=∠VUT

From the given figure ,∠UVS is 25°.Putting the values in the given equation, we get

$90+25=$∠VUT

∠VUT = 115 = a

Therefore the value of a is 115° and b is 40°.

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Thank you