Question

find the answer pls. ​

Answer 1

Step-by-step explanation:

Solution :-

Given that

DE || FG and IJ is a transversal

<JCG = 70°

Now,

<JCG and <ACG are linear pair

=> <JCG + <ACG = 180°

=> 70° + <ACG = 180°

=> <ACG = 180° -70°

=> <ACG = 110°

and

<IAK and <CAB are vertically opposite angles which are equal.

=> <IAK = <CAB

=> x° = <CAB

=> <CAB = x°

and

<CAB and <CAE are complementary angles

=> <CAB + <CAE = 90°

=> x° + <CAE = 90°

=> <CAE = 90°-x°

Now,

<CAE and <ACG are the interior angles on the same side to the transversal.

=> <CAE + <ACG = 180°

=> 90°-x° + 110° = 180°

=> 200° -x° = 180°

=> -x° = 180°-200°

=> -x° = -20°

=> x° = 20°

Therefore, <x = 20°

Answer :-

The measure of x for the given problem is 20°

Used formulae:-

If two parallel lines are interested by a transversal then,

→ vertically opposite angles are equal.

→ the interior angles on the same side to the transversal.

→ The sum of two adjacent angles is 180° then they are called a linear pair.

→ The sum of two angles is 90° then they are Complementary angles.

Answer 2

Answer:

∠x = 20°

Step-by-step explanation:

Inorder to solve this problem, we have knowledge about parallel lines, transversal and properties of parallel lines.

Two lines are said to be parallel, if the distance between those lines remain same even extending both lines upto infinity.

A transversal is a line, which intersects two parallel lines.

Some properties or parallel lines includes :-

• Alternate interior angles are always equal.
• Alternate exterior angles are always equal.
• Sum of co interior angles is always 180°.
• Corresponding angles are always equal.

Now, let's solve the given problem!

Consider the parallel lines FG and DE and IJ be the transversal.

By the property of alternate exterior angles, we get ;

➝ ∠ JCG = ∠ DAI = 70° ______( Equation 1 )

Given that parallel lines and transversal KL are Perpendicular to each other.

Now consider parallel lines FG and DE and KL be the transversal.

➝ ∠ ABF = ∠ KAD = 90° ( By corresponding angles )

∠ KAD is made up of two angles which are ∠DAI and ∠ KAI.

Therefore,

➝ ∠ KAD = ∠ KAI + ∠ DAI

➝ 90° = x + 70° ‎ ‎ ‎ ‎ ‎ ‎( By using equation 1 )

➝ 90° - 70° = x

➝ 20° = x

Hence the value of x is 20°