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 = 65° m∠DBC = ? m∠DCB = ? m∠CDB = ? m∠ACD = ? m∠ADC = ?

Answer:Part 1) m∠DBC=25°Part 2) m∠DCB=65°Part 3) m∠CDB=90°Part 4) m∠ACD=25°Part 5) m∠ADC=90°Step-by-step explanation:see the attached figure to better understand the problemstep 1Find the measure of angle DBCwe know thatThe sum of the interior angles of a triangle must be equal to 180 degreesIn the right triangle ABCm∠A+m∠B+m∠C=180° ----> equation Awe havem∠A=65° ----> given problemm∠C=90° ----> given problemSubstitute the given values in the equation A and solve for m∠B65°+m∠B+90°=180°m∠B+155°=180°m∠B=180°-155°m∠B=25°Remember that the measure of Angle B is equal to say the measure of angle DBCsom∠B=m∠DBCthereforem∠DBC=25°step 2 Find the measure of angle DCB and angle CDBIn the right triangle DBCThe sum of the interior angles of a triangle must be equal to 180 degreesm∠DBC+m∠DCB+m∠CDB=180°we havem∠DBC=25°m∠CDB=90° ----> is a right angle (CD is the height to AB)substitute the values and solve for m∠DCB25°+m∠DCB+90°=180°m∠DCB+115°=180°m∠DCB=180°-115°=65°step 3Find the measure of angle ACDwe know thatm∠ACD+m∠DCB=90° -----> by complementary angleswe havem∠DCB=65°substitute the valuem∠ACD+65°=90°m∠ACD=90°-65°=25°step 4Find the measure of angle ADCm∠ADC=90° ----> is a right angle (CD is the height to AB)