Question

How to solve this i have a exam help me! i have attached the picture help me!​

Answer 1

Will recommend to keep in touch with attached picture while reading Answer as names of angles are written according to attached picture!

$\rm\angle BAO = \angle DCO$

Reason:-

Alternate Interior Angles.

What is Alternate Interior Angles.?

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.

Remember this only possible as lines are parallel give. We get to know that lines are parallel as upward arrow is marked in that lines.

$\rm \therefore\angle DCO = 2a \degree$

Now Let's find angle DOC.

$\rm\angle DOC +\angle DOA = 180\degree$

Reason:-

LP (Linear Pair)

What is LP (Linear Pair) ?

Linear pair of angles are formed when two lines intersect each other at a single point

So let's solve:-

$\hookrightarrow \rm\angle DOC +\angle DOA = 180\degree$

$\hookrightarrow \rm78 \degree +\angle DOC= 180\degree$

$\hookrightarrow \rm\angle DOC = 180\degree - 78 \degree$

$\hookrightarrow \rm\angle DOC =102\degree$

Finally Let's find value of a.

$\rm\angle CDO + \angle DCO + \angle DOC = 180°$

reason:-

Sum of angles triangle = 180°

Formula to find :

• (number of angles - 2) × 180°
• (3 - 2) × 80°
• 1 × 180°
• 180°

So let's find:-

$\dashrightarrow \rm\angle CDO + \angle DCO + \angle DOC = 180°$

$\dashrightarrow \rm2a + a+ 102= 180°$

$\dashrightarrow \rm3 a+ 102= 180°$

$\dashrightarrow \rm3 a= 180° - 102$

$\dashrightarrow \rm3 a= 78°$

$\dashrightarrow \rm a= 78° \div 3$

$\dashrightarrow \bf a= 26°$

Now Let's find angle b

angle b = angle a

Reason:-

Alternate Interior Angles.

Therefore angle b = 26°

Answer 2

The unknown angles formed when the two transversal cuts the parallel lines are 26°, 26° and 52°.

Angles formed when transversals line cuts parallel lines.

When two or more lines are cut by a transversal, the angles formed includes corresponding angles, alternate angles etc.

Therefore,

a = b (alternate angles)

Hence,

2a + b + (180 - 78) = 180 (sum of angles in a triangle)

2a + a + 102 = 180

3a + 102 = 180

3a = 180 - 102

3a = 78

a = 78 / 3

a = 26

Therefore, the unknown angles are 26°, 26°, and 2(26) = 52°

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