Find the angles marked with letters. (AB is always a straight line)
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Answer:
25° = e
Step-by-step explanation:
CD = DB ......given
ANGLE ABD = ANGLE DCB.... isosceles triangle theorem
THEREFORE, ANGLE DCB = 65°.....(1)
SINCE, ANGLE CDA IS AN EXTERIOR AMGLE OF TRIANGLE CDB
THEREFORE,
ANGLE DBC + ANGLE DCB = ANGLE CDA ..... remote interior angle theorem
THEREFORE,
65°+65° = ANGLE CDA = 130°...... FROM 1.......(2)
IN TRIANGLE CDA, AD = DC
THEREFORE, ANGLE DAC = ANGLE DCA .....isosceles triangle theorem
THEREFORE, ANGLE DCA = e.......(3)
IN TRIANGLE ADC,
ANGLE DAC + ANGLE DCA + ANGLE CDA = 180°.....SUM OF ANGLES OF A TRIANGLE IS 180°
THEREFORE,
e + 130 + e = 180°........from (2) and (3)
2e = 180 - 130
e = 50/2
e = 25°
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