Question

Triangles ACD and BCD are isosceles. Angle BAC has a measure of17 degrees and angle BDC has a measure of 52 degrees. Match thefollowing angles with their correct measurement.

Answer 1

∠BCD = 52°

∠CBD = 76°

m∠DAC = 34°

m∠DBA = 142°

m∠ADC = 73°

m∠BAD = 17°

Explanation:

Given:

m∠BAC = 17°

m∠BDC = 52°

Considering triangle DBC:

two sides of the triange are equal. Hence, the base angles will be equal.

The base angls are ∠BDC and ∠BCD

∠BDC = ∠BCD

∠BCD = 52°

∠BDC + ∠BCD + ∠CBD = 180° (angles in a triangle)

52 + 52 + ∠CBD = 180°

104 + ∠CBD = 180°

∠CBD = 180 - 104

∠CBD = 76°

B bisects angle ∠DAC. This divides it into two equal halves.

m∠BAC = m∠BAD, m∠BAC = 17

m∠BAD = 17°

m∠DAC = m∠BAC + m∠BAD

m∠DAC = 17 + 17 = 34°

m∠CDB + m∠DBA + m∠CBA = 360° (angles at a point)

m∠DBA = m∠CBA (side AD = ide AC)

Angles opposite the sides will also be equal

76 + 2(m∠DBA) = 360

2(m∠DBA) = 360 - 76

2(m∠DBA) = 284

m∠DBA = 284/2

m∠DBA = 142°

m∠ADC = m∠ADB + m∠BDC

m∠ADB + m∠DBA + m∠BAD = 180° (angles in a triangle)

m∠ADB + 142 + 17 = 180

m∠ADB + 159 = 180

m∠ADB 180 - 159

m∠ADB = 21°

m∠ADC = 21 + 52

m∠ADC = 73°