Question

if triangle ADE ~ triangle ACB, angle DEC =105 and angle ECB= 65 , then value of x is

Answer 1

Answer:

PAB=60 AB=50cm CB=40cm angle ADP =90​

Step-by-step explanation:

Answer 2

Similar triangles

Given:

$\triangle ADE \sim \triangle ACB\\\angle DEC=105\textdegree\\\angle ECB=65\textdegree$

To find:

The value of x

Explanation:

If two triangles are similar then their corresponding angles are congruent and the corresponding sides are in proportion.

According to the figure attached and the information provided,

$\therefore \frac{AD}{AC} =\frac{DE}{CB} =\frac{AE}{AB}$

and corresponding angles,

$\angle D\cong \angle C\\And\\\angle E\cong \angle B$

so,

$\angle AED=180\textdegree-105\textdegree(linear\ pair)\\\angle AED=75\textdegree$

So, $\angle ADE=\angle ACB=65 \textdegree$

Hence in ΔADE,

$\angle ADE+\angle AED+\angle DAE=180\textdegree(sum \ of\ all \ the \ angles\ of \ a \ triangle\ is \ 180)\\\\\implies 65\textdegree+75\textdegree+\angle x=180\textdegree\\\\ \implies \angle x =40\textdegree$

Hence the value of x is 40°.