Question

Find m angle BCA. please help if you can!!

Answer 1

• m∠BCA = 57°

Explanation:

`\tt 10x+37+9x+1+5x+12=360^o`

Add like terms:-

`\tt 10x+9x+5x=360^o+37^o-1^o-12^o`

`\tt 10x+9x+5x=\bf 24x`

`\tt 360+37-1-12=\bf 384`

`\tt 24x=384`

Divide both sides by 24:-

`\tt \cfrac{24x}{24}=\cfrac{384}{24}`

`\tt x=16^o`

Now, let's find m∠BCA:-

m∠BCA = 180-(10x-37)

`\tt 180-(10(16)-37)`

`\tt 180-123`

`\tt 57^o`

Therefore, m∠BCA = 57°.

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Hope this helps!

Answer 2

• m∠BCA = 57°

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Sum of exterior angles measures is 360°.

Set up the following equation and solve for x:

• 9x + 1 + 5x + 12 + 10x - 37 = 360
• 24x - 24 = 360
• 24x = 384
• x = 384/24
• x = 16

Find exterior angle measure at vertex C:

• 10*16 - 37 = 160 - 37 = 123°

We know interior and exterior angles on the same vertex form a linear pair.

Find interior angle at vertex C, the ∠BCA:

• m∠BCA = 180° - 123° = 57°