Question

find the angle measure xin the following figure 30°,70°,60°,X,X​

Answer 1

Step-by-step explanation:

70+y=180 (linear pair)

y=180-70

y=110°

60+z=180 (linear pair)

z=180-60

z=120°

30+x+x+y+z=540

30+2x+110+120=540°

2x+260=540°

2x=540-260

2x=280

x=280/2

x=140°

Answer 2

To Find :- The measure of ∠x in the following figure .

Solution :-

Denote the vertices of given figure as A, B, C, D and E .

now,

→ ∠BCD = 180° - 70° { Linear pair }

→ ∠BCD = 110°

similarly,

→ ∠EDC = 180° - 60° { Linear pair }

→ ∠EDC = 120°

also,

→ ∠BAE = 30° { given }

now, we know that,

• Sum of Interior angles of a polygon with n sides = (n - 2) × 180° .

So,

→ Sum of interior angles of pentagon ABCDE = (5 - 2) × 180°

→ ∠BCD + ∠EDC + ∠BAE + x + x = 3 × 180°

putting all values from above,

→ 110° + 120° + 30° + 2x = 540°

→ 260° + 2x = 540°

→ 2x = 540° - 260°

→ 2x = 280°

dividing both sides by 2,

→ x = 140° (Ans.)

Hence, The measure of ∠x in the following figure is equal to 140° .

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