Question

Find the values of x, y, z in the following diagram:​

Answer 1

Answer:

Sorry

Step-by-step explanation:

I Don't Understand

Answer 2

$\huge\fbox \red{✔AN} {\colorbox{crimson}{SW}}\fbox\red{ER✔}$

$\Large{\textsf{\textbf{\underline{\underline{To\:Find\::}}}}}$

Value of x.

Value of y.

Value of z.

$\Large{\textsf{\textbf{\underline{\underline{Solution\::}}}}}$

As we know that,

☆ If two sides of a triangle are equal, then their corresponding angles are also equal to each other.

In ∆ABC,

$: \: \leadsto \rm{BC\:=\:AC}\quad (Given)$

Thus,

✔ Their corresponding angles are also equal.

$\dashrightarrow\:\tt{\angle{BAC}\:=\:\angle{ABC}\:}$

According to the question,

$\rm{\angle{BAC}\:=\:32^{\circ}\:}$

$: \: \leadsto \rm{\angle{ABC}\:=\:x\:=\:32^{\circ}\:}$

$: \: \leadsto \bf \green{x\:=\:32^{\circ}\:}$

Again,

In ∆ABC,

$: \: \leadsto \rm{\angle{BAC}\:+\:\angle{ABC}\:+\:\angle{ACB}\:=\:180^{\circ}\:}$

$: \: \leadsto \rm{32^{\circ}\:+\:32^{\circ}\:+\:\angle{ACB}\:=\:180^{\circ}\:}$

$: \: \leadsto \rm{64^{\circ}\:+\:\angle{ACB}\:=\:180^{\circ}\:}$

$: \: \leadsto \rm{\angle{ACB}\:=\:180^{\circ}\:-\:64^{\circ}\:}$

$: \: \leadsto \bf {\angle{ACB}\:=\:116^{\circ}\:}$

As we know that,

Angle made by a straight line is always 180°.

$: \: \leadsto \rm{\angle{ACB}\:+\:y\:=\:180^{\circ}\:}$

$: \: \leadsto \rm{116^{\circ}\:+\:y\:=\:180^{\circ}\:}$

$: \: \leadsto \rm{y\:=\:180^{\circ}\:-\:116^{\circ}\:}$

$: \: \leadsto {\bf{\green{y\:=\:64^{\circ}\:}}}$

Now,

In ∆BCD,

$\longrightarrow\:{\tt{BC\:=\:BD}}~~~(Given)$

$\longrightarrow\:\tt{\angle{BDC}\:=\:y\:}$

$\longrightarrow\:\tt{\angle{BDC}\:=\:64^{\circ}\:}$

Again,

In ∆BCD,

$: \: \leadsto \rm{\angle{BDC}\:+\:y\:+\:z\:=\:180^{\circ}\:}$

$: \: \leadsto \rm{64^{\circ}\:+\:64^{\circ}\:+\:z\:=\:180^{\circ}\:}$

$: \: \leadsto \rm{128^{\circ}\:+\:z\:=\:180^{\circ}\:}$

$: \: \leadsto \rm{z\:=\:180^{\circ}\:-\:128^{\circ}\:}$

$: \: \leadsto\:{\bf{\green{z\:=\:52^{\circ}\:}}}$