Question

find the missing angles​

Answer 1

Answer:

solution is in the attachment

Answer 2

Answer:

Step-by-step explanation:

fig 1

angle Y + angle X =  angle XZT   [ exterior angle sum property ]

              60   +   x = 2x + 4

                 60 - 4 = x

                   56= x

and 2x + 4 = 56 * 2 + 4 = 116

now,

angle X + angle Y + angle Z = 180°   [ triangle sum property ]

56 + 60 + angle Z = 180

                angle Z = 180 - 116 = 64

FIG 2.

GIVEN - AB = AC

angle B = angle C  [ANGLE OPPOSITE TO EQUAL SIDE ARE EQUAL]

let angle B and C = x

130 ° + angle B = 180°  [ linear pair axiom ]

          angle B = 180-130 = 50°

angle C = 50°  [ angle B = angle C ]

NOW triangle ABC

angle A +angle B +angle C       = 180   [ triangle sum property ]

angle A = 180 - 100 = 80°

IN triangle ACD

angle Y = angle Z  [ angle opposite to equal side are equal]

angle  ACB = angle Y + angle Z  [ exterior angle sum property ]

              50° = X +X

              25 = X

SO angle Y = angle Z = 25°

NOW angle X + angle BAC + angle Y = 180°  [linear pair axiom]

                        angle X + 80 + 25 =180

                                   angle X = 180 -105 = 75°

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