Question

Angles are not necessarily drawn to scale find x​

Answer 1

Answer: Angle x = 78°

Step-by-step explanation: The entire diagram upon careful observation, shows several triangles intercepting one another. One of such triangles is triangle BDH. It has three angles with two of them clearly marked as angle B (47°) and angle D (31°). Angle H is unknown but we can calculate this as

B + D + H = 10° {Sum of angles in a triangle equals 180}

47 + 31 + H = 180

78 + H = 180

H = 180 -78

H = 102°

However, angle x and angle H both lie on a straight line which is BIHC

At the intersection labeled H,

Angle x + angle H = 180 {Sum of angles on a straight line equals 180}

Therefore,

Angle x + 102 = 180

Subtract 102 from both sides of the equation

x = 78°

Answer 2

Answer:

x=61

Step-by-step explanation:

From the diagram, we see that \angle XOY∠XOYangle, X, O, Y and \angle YOZ∠YOZangle, Y, O, Z are complementary angles.

Therefore, m \angle XOY + m \angle YOZ = 90^\circm∠XOY+m∠YOZ=90  

∘

m, angle, X, O, Y, plus, m, angle, Y, O, Z, equals, 90, degrees.

\begin{aligned}\angle XOY + \angle YOZ &= 90^\circ \\\\ 29+x &= 90 \\\\ x &= 61^\circ \end{aligned}  

∠XOY+∠YOZ

29+x

x=90

x=61

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