Question

Find the measurement of ∠A from given figure.​

Answer 1

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Answer 2

Given :-

• ∠ABC = 65°
• ∠ACD = 115°

To Find :-

• ∠BAC = ?

For Knowledge :-

• As we know ∠BCA + ∠ACD = 180°
• And ∆ ABC = 180°
• ∆ ABC = ∠ACB + ∠CBA + ∠BAC = 180°

Required Answer :-

• First of all we find the angle of C
• hence we can use this formula ∠BCA + ACD = 180°

$\large \tt{∠BCA +∠ ACD = 180° } \\ \\ \large \tt{ ∠BCA + 115 \degree = 180 \degree} \\ \\ \large \tt{ ∠BCA = 180 \degree - 115 \degree} \\ \\ \large \tt{ \fbox{∠BCA = 65 \degree }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

• Now finally we find the ∠BAC
• hence we can use this formula
• ∆ ABC = ∠ACB + ∠CBA + ∠BAC = 180°

$\large \tt {∠BCA + ∠ABC + ∠BAC = 180° } \\ \\ \large \tt {65 \degree + 65 \degree +∠A = 180\degree \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \large \tt {130 \degree +∠A = 180 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \large \tt {∠A = 180\degree - 130\degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \tt { \fbox{∠A =50\degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

I hope it helps you ❤️✔️