Question

Please solve this step by step :)

Answer 1

Answer:

M + 63 = 136 (external angle property)

M = 73 degree

Answer 2

Question:

Find the value of $\bold{m}$ in the figure.

Given:

• $\angle ABC={63}^{o}$
• $\angle ACD={136}^{o}$

To Find:

• Value of $\bold{m}$

Solution:

We have, ∆ABC with an exterior angle $\angle ACD$. For finding the value of m. We firstly need to find interior angle $\angle C$.

$\angle BCD$ is an straight angle. So,

$\rightarrow\mathsf{\angle BCA+\angle ACD={180}^{o}}$

$\rightarrow\mathsf{\angle BCA+{136}^{o}={180}^{o}}$

$\rightarrow\mathsf{\angle BCA={180}^{o}-{136}^{o}}$

$\rightarrow\mathsf{\angle BCA={44}^{o}}$

Now, ABC is a triangle. So, sum of all three angle in the triangle is 180°. Therefore,

$\dashrightarrow\mathsf{\angle ABC+\angle BCA+\angle CAB={180}^{o}}$

$\dashrightarrow\mathsf{{63}^{o}+{44}^{o}+m={180}^{o}}$

$\dashrightarrow\mathsf{{107}^{o}+m={180}^{o}}$

$\dashrightarrow\mathsf{m={180}^{o}-{107}^{o}}$

$\dashrightarrow\mathsf{m={73}^{o}}$

Hence, the value of m in ∆ABC is 73°.

Alternative Method:

We know, that sum of two opposite interior angle is equal to exterior angle. Therefore,

$\rightarrow\mathsf{\angle BAC+\angle ABC=\angle ACD}$

$\rightarrow\mathsf{m+{63}^{o}={136}^{o}}$

$\rightarrow\mathsf{m={136}^{o}-{63}^{o}}$

$\rightarrow\mathsf{m={73}^{o}}$

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