Mathematics: Find the m∠cde, if m∠bac = 55° and ∠bca is a right angle. 35° 45° 55° 90°

Find the m∠cde, if m∠bac = 55° and ∠bca is a right

mystaxkkks

15.03.2022

$m\angle CDE=35^o$

Step-by-step explanation:

We have been given an image of two triangles.

Since segment AB is parallel to segment CD and segment BC is parallel to segment DE.

We can see that segment AE is transversal for our given triangles.

Since corresponding angles of two parallel formed by a transversal are always equal.

We can see that $\angle ABC$ corresponds to angle $\angle CDE$ .

$m\angle ABC=m\angle CDE$

Let us find measure of angle ABC using angle sum property.

$\angle ABC+\angle BAC+\angle BCA=180^o$

$\angle ABC+55^o+90^o=180^o$

$\angle ABC+145^o=180^o$

$\angle ABC+145^o-145^o=180^o-145^o$

$\angle ABC=35^o$

Therefore, measure of angle CDE is 35 degrees.

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