Question

Find the values of x and y using the information shown in figure. Find the measure of $\angle$ABD and
$\angle$ACD.

Answer 1

In $△$ABC,
seg AB = seg AC [given}
$\angle$ACB = ${50}^{\circ }$ [Given]
x = $\angle$ACB =${50}^{\circ }$ [Isoceles angle theorem]
In $△$ BCD,
seg BD = seg CD [Given]
y = $\angle$CBD = ${60}^{\circ }$ [Isoceles angle theorem]
Hence measure of x and y are ${50}^{\circ }and{60}^{\circ }$ respectively.
$\angle$ABD = x + $\angle$CBD [angle addition property]
$\angle$ABD = ${50}^{\circ }+{60}^{\circ }={110}^{\circ }$
$\angle$ACD = $\angle$ACB + $\angle$y [Angle addition property]
$\angle$ACD = ${50}^{\circ }+{60}^{\circ }={110}^{\circ }$
Hence measure of $\angle$ACD is ${110}^{\circ }$