Answer:
A. 23+x=140
Step-by-step explanation:
The angle addition postulate states that the measure of a larger angle formed by two or more smaller angles placed side by side is the the sum of the smaller angles. The angle addition postulate states that if B is in the interior of AOC , then:
m∠AOB + m∠BOC = m∠AOC.
From the image:
∠NOP = ∠NOQ + ∠QOP
∠NOP = 140, ∠NOQ = x, ∠QOP = 23
substituting:
140 = x + 23
x = 140 - 23 = 117
∠NOQ = 117°
Answer:
B
Step-by-step explanation:
First calculate BD using sine ratio in Δ BCD and the exact value
sin60° = , thus
sin60° = =
=
=
( cross- multiply )
2BD = 12 ( divide both sides by 2 )
BD = 6
-----------------------------------------------------------
Calculate AD using the tangent ratio in Δ ABD and the exact value
tan30° = , thus
tan30° = =
=
=
( cross- multiply )
AD = 6
( divide both sides by
)
AD = 6 → B