Question

Find the angles marked with letters. (AB is always a straight line)

Answer 1

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°