Question

in the figure shown ∠bxd is a right angle and ∠axe is a straight angle. if m(∠bxc)=55° and m(∠bxe)=131°, determine the measures of ∠axb, ∠cxd, and ∠dxe without using a protractor
note that the figure is not drawn to scale.

the measure of ∠axb is □°
(simplify your answer )
the measure of ∠cxd is □°
(simplify your answer )
the measure of ∠dxe is □°
(simplify your answer.)

Explanation:

Step1: Find $m\angle AXB$

$\angle AXE$ is straight ($180^\circ$), so:
$$m\angle AXB = 180^\circ - m\angle BXE = 180^\circ - 131^\circ = 49^\circ$$

Step2: Find $m\angle CXD$

$\angle BXD$ is right ($90^\circ$), so:
$$m\angle CXD = 90^\circ - m\angle BXC = 90^\circ - 55^\circ = 35^\circ$$

Step3: Find $m\angle DXE$

First find $m\angle EXB = 131^\circ$, subtract $\angle BXD$:
$$m\angle DXE = 131^\circ - 90^\circ = 41^\circ$$

Answer:

The measure of $\angle AXB$ is $49^\circ$
The measure of $\angle CXD$ is $35^\circ$
The measure of $\angle DXE$ is $41^\circ$