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Complete.

4. In the diagram, m1=?and m2=?

Short Answer

Expert verified

In the diagram, m1=105andm2=35

Step by step solution

01

Step 1. Draw a labelled diagram.

The labelled diagram is:

02

Step 2. Description of step.

From the diagram it can be noticed that:

BAD=BAC+CAD

Therefore, it can be obtained that:

BAD=BAC+CAD=50°+40°=90°

Therefore, the measure of the angle BADis 90°.

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

Therefore, the sum of the angles of a triangle ΔABDis 180°.

Therefore, it can be obtained that:

BAD+ABD+ADB=180°90°+55°+2=180°145°+2=180°

2=180°145°2=35°

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

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

Therefore, the sum of the angles of a triangle ΔACDis 180°.

Therefore, it can be obtained that:

CAD+ACD+ADC=180°40°+2+1=180°40°+35°+1=180°75°+1=180°1=180°75°1=105°

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

03

Step 3. Write the complete statement.

In the diagram, m1=105and m2=35.

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