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ICE Princess25 [194]
3 years ago
11

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°

Mathematics
2 answers:
marishachu [46]3 years ago
5 0

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°.

Igoryamba3 years ago
4 0
 triangle CBD = 180-20-90=70
trangle CAD=20
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