Question

can anyone solve this step by step​

Answer 1

∠ABC = 130°

Step-by-step explanation:

Given:-

• DE is parallel to BA.
• ∠C = 50°.
• ∠D = 100°.

To find :-

• Measure of ∠ABC

Solution:-

• Construct a line MN parallel to AB.

If MN is parallel to AB and AB is parallel to DE. Then, MN is also parallel to DE.

We know that,

Sum of two angles lie between two parallel lines on same side of transversal is 180°. This statement is also known as Co - interior angles.

So,

➝ ∠D + ∠DCN = 180° [Co - interior angle]

➝ 100° + ∠DCN = 180°

➝ ∠DCN = 180° - 100°

➝ ∠DCN = 80°

We also know that,

Sum of all angles forms on straight line is equal to 180°. This statement is also known as linear pair.

So,

➝ ∠BCM + ∠BCD + DCN = 180° [Linear pair]

➝ ∠BCM + 50° + 80° = 180°

➝ ∠BCM + 130° = 180°

➝ ∠BCM = 180° - 130°

➝ ∠BCM = 50°

Now,

➝ ∠ABC + ∠BCM = 180° [Co - interior angle]

➝ ∠ABC + 50° = 180°

➝ ∠ABC = 180° - 50°

➝ ∠ABC = 130°

Therefore,

∠ABC is of 130°.