Chapter 7.1, Problem 21PSC

To determine

To calculate : The value of $m\angle A$ .

Answer to Problem 21PSC

The value of $m\angle A$ is $\frac{{180}^0}{7}$

Explanation of Solution

Given information : The following information is given

  $\overrightarrow{AB}\cong \overrightarrow{AC}$

  $\overrightarrow{AE}\cong \overrightarrow{DE}\cong \overrightarrow{DB}\cong \overrightarrow{BC}$

Formula used : Sum of the angles of any triangle is ${180}^0$

Calculation : in the $\Delta ABC$ , let

  $\angle CAB=a$ , and $\angle ACB=\angle ABC=c$

Now, if $\angle CAB=a$ , then we have

  $\angle ADE=\angle CAB=a$

  $\angle AED={180}^0-2a$

  $\angle DEB={180}^0-({180}^0-2a)=2a$

  $\angle DBE=\angle DEB=2a$

  $\angle EDB={180}^0-(4a)$

  $\angle BCD=\angle BDC=c$

  $\angle DBC={180}^0-(2c)$

Now,$\angle ABD+\angle DBC=\angle ABC$

Thus,$({180}^0-2c)+2a=c$

Also, $\angle ADE+\angle EDB+\angle BDC={180}^0$

Thus,${180}^0=a+({180}^0-4a)+c$

Now, solving ${180}^0=a+({180}^0-4a)+c$ and $({180}^0-2c)+2a=c$ linear equations for a and c , we get

  $a=\frac{{180}^0}{7}$