Answer:
The measure of angle B is 70°.
The measure of angle DCB is 20°.
The measure of angle DCA is 70°.
Step-by-step explanation:
Given information: In triangle ΔABC, m∠A = 20°, ∠C is a right angle and CD is the height to AB.
It means CD⊥AB and [tex]\angle ACB=90^{\circ}[/tex].
[tex]\angle CDA=\angle CDB=90^{\circ}[/tex]
According to the angle sum property, the sum of all interior angles of a triangle is 180°.
In triangle ABC,
[tex]\angle A+\angle B+\angle C=180[/tex]
[tex]20+\angle B+90=180[/tex]
[tex]\angle B+110=180[/tex]
[tex]\angle B=180-110[/tex]
[tex]\angle B=70[/tex]
Therefore, the measure of angle B is 70°.
In triangle CBD,
[tex]\angle CBD+\angle BDC+\angle DCB=180[/tex]
[tex]70+90+\angle DCB=180[/tex]
[tex]160+\angle DCB=180[/tex]
[tex]\angle DCB=180-160[/tex]
[tex]\angle DCB=20[/tex]
Therefore, the measure of angle DCB is 20°.
n triangle CAD,
[tex]\angle CAD+\angle ADC+\angle DCA=180[/tex]
[tex]20+90+\angle DCA=180[/tex]
[tex]110+\angle DCA=180[/tex]
[tex]\angle DCA=180-110[/tex]
[tex]\angle DCA=70[/tex]
Therefore, the measure of angle DCA is 70°.
