Question

12.) Find the value of x and y. Show ALL work.

Answer 1

Answer: The value of x = 90°

and the value of y = 43°

Step-by-step explanation:

Since we have given that

In ΔABC,

∠B=∠C=47°

As we know that "Sum of all three angles of a triangle is 180° ".

So, it becomes,

$\angle A+\angle B+\angle C=180\textdegree\\\\\angle A+47\textdegree+47\textdegree=180\textdegree\\\\\angle A+94\textdegree=180\textdegree\\\\\angle A=180\textdegree-94\textdegree\\\\\angle A=86\textdegree\\\\So,\\\\y=\frac{86}{2}=43\textdegree$

Similarly,

Now, in ΔABD,

$\angle A+\angle B+\angle ADB=180\textdegree\\\\43\textdegree+47\textdegree+\angle ADB=180\textdegree\\\\90\textdegree+\angle ADB=180\textdegree\\\\\angle ADB=180\textdegree-90\textdegree\\\\\angle ADB=90\textdegree$

Hence, the value of x = 90°

and the value of y = 43°