Question

In triangle ΔABC, ∠C is a right angle and CD is the height to AB , Find the angles in ΔCBD and ΔCAD if: m∠A = 20°

Answer 1

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 $\angle ACB=90^{\circ}$.

$\angle CDA=\angle CDB=90^{\circ}$

According to the angle sum property, the sum of all interior angles of a triangle is 180°.

In triangle ABC,

$\angle A+\angle B+\angle C=180$

$20+\angle B+90=180$

$\angle B+110=180$

$\angle B=180-110$

$\angle B=70$

Therefore, the measure of angle B is 70°.

In triangle CBD,

$\angle CBD+\angle BDC+\angle DCB=180$

$70+90+\angle DCB=180$

$160+\angle DCB=180$

$\angle DCB=180-160$

$\angle DCB=20$

Therefore, the measure of angle DCB is 20°.

n triangle CAD,

$\angle CAD+\angle ADC+\angle DCA=180$

$20+90+\angle DCA=180$

$110+\angle DCA=180$

$\angle DCA=180-110$

$\angle DCA=70$

Therefore, the measure of angle DCA is 70°.

Answer 2

 triangle CBD = 180-20-90=70
trangle CAD=20