Question

What is the measure of \blueD{\angle x}∠xstart color #11accd, angle, x, end color #11accd?
Angles are not necessarily drawn to scale.




\blueD{\angle x}∠xstart color #11accd, angle, x, end color #11accd ==equals
\Large{{}^\circ}
∘

Answer 1

Answer:

x = 78°

Step-by-step explanation:

From the picture attached,

From ΔBHD,

m∠DBH + m∠BDH + m∠BHD = 180°

47° + 31° + m∠BHD = 180°

m∠BHD = 180° - 78°

m∠BHD = 102°

Since, ∠BHD and ∠BHC are the linear pair of angles,

m∠BHD + m∠BHC = 180°

102° + m∠BHC = 180°

m∠BHC = 180° - 102°

x° = 78°

Answer 2

The measure of the angle x from the diagram is 78 degrees

From the diagram, the sum of angle in thee interior angle of the triangle BDH is 180 degrees hence;

m<B + m<D +m<H= 180

47 + 31 + m<BHD = 180

78 + m<BHD = 180

m<BHD = 180 - 78

m<BHD = 102 degrees

Next is to get the unknown value "x"

The sum of angle on the straight line DHC is 180 degrees. Hence:

m<BHD + x = 180

x = 180 - m<BHD

x = 180 - 102

x = 78 degrees

Hence the measure of the angle x from the diagram is 78 degrees

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