angle ACB=90° angle ABC=20° and angle CAD =angle DAB what is the measure of angle ADC
no idea. Where is D?
To find the measure of angle ADC, we can use the given information and apply the properties of angles in a triangle. Here are the steps to solve it:
Step 1: Draw the triangle ABC with points A, B, and C, and construct line segments AD and CD.
Step 2: Given that angle ACB is a right angle (90°), label it as 90°.
Step 3: Given that angle ABC is 20°, label it as 20°.
Step 4: Given that angle CAD is equal to angle DAB, and since triangle CAD and triangle DAB share a common side AD, we can consider them congruent by the Angle-Side-Angle (ASA) Congruence Postulate.
Step 5: Draw points D and E on line segment BC such that DE is perpendicular to BC.
Step 6: Now, since triangle CAD and triangle DAB are congruent, angle CDA is congruent to angle DBA.
Step 7: Therefore, angle ADC can be found by subtracting the sum of angle ACB (90°) and angle ABC (20°) from 180° (the sum of angles in a triangle).
So, angle ADC = 180° - (90° + 20°)
= 180° - 110°
= 70°
Therefore, the measure of angle ADC is 70°.