Question

line AB is parallel to line CD and line CD is parallel to line EF lone QP is their transversal. if y:z=3:7 then find the measure of angle x,angle y and angle z​.

pls. give correct answer.......​

Answer 1

Answer:

X= 126

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Answer 2

Given,

Line AB || line CD || line EF

Line QP is the transversal

Angle y: angle z = 3:7

To find,

The measure of angle x, angle y, and angle z.

Solution,

We can simply solve this mathematical problem using the following process:

Geometrically,

If two lines are parallel and a transversal cuts then, then,

a) the two interior angles formed on the same side of the transversal are supplementary

b) the measure of vertically opposite angles is equal

{Statement-1}

Let us assume that the angle opposite to angle y is w.

Also, let angle y is 3a° and angle z is 7a°.

Now, according to the question and statement-1;

angle x + angle y = 180°

{Equation-1}

And,

angle y = angle w = 3a°

{Equation-2}

Also, angle w + angle z = 180°

=> 3a° + 7a° = 180°

=> 10a = 180

=> a = 18

Now,

the measure of angle y = 3a°

= 3×18 = 54°

the measure of angle z = 7a°

= 7×18 = 126°

Now, according to equation-1;

angle x + angle y = 180°

=> angle x + 54° = 180°

=> angle x = 126°

Hence, the measure of angle x and z is 126° and the measure of angle y is 54°, respectively.