91Ó°ÊÓ

The labelled diagram is:

From the diagram, it can be noticed that:

$∠BAD=∠BAC+∠CAD$

Therefore, it can be obtained that:

$$\begin{gathered} ∠BAD=∠BAC+∠CAD \\ =50°+40° \\ =90° \end{gathered}$$

Therefore, the measure of the angle∠BAD is 90°.

The sum of the angles of a triangle is 180°.

Therefore, the sum of the angles of a triangleΔABD is 180°.

Therefore, it can be obtained that:

$$\begin{gathered} ∠BAD+∠ABD+∠ADB=180° \\ 90°+55°+∠2=180° \\ 145°+∠2=180° \\ ∠2=180°−145° \\ ∠2=35° \end{gathered}$$

Therefore, the measure of the angle∠2 is 35°.

The sum of the angles of a triangle is 180°.

Therefore, the sum of the angles of a triangleΔACD is 180°.

Therefore, it can be obtained that:

$$\begin{gathered} ∠CAD+∠ACD+∠ADC=180° \\ 40°+∠2+∠1=180° \\ 40°+35°+∠1=180° \\ 75°+∠1=180° \\ ∠1=180°−75° \\ ∠1=105° \end{gathered}$$

Therefore, the measure of the angle ∠1 is 105°.

In the diagram, $m∠1=105$and $m∠2=35$.