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In the kite WEAR shown below, $∠ W E A = 70 ∘$ and $∠ A R W = 8 0 ∘$ and . Determine the angle measures of the remaining two angles.

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105 ∘, 105 ∘

95 ∘, 95 ∘

55 °, 55 ∘

110 ∘, 110 ∘

answer is A.

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Detailed Solution

Here, we are given a kite with its two angle measures as

∠ W E A = 70 ∘

and

∠ A R W = 8 0 ∘

, as shown in the diagram above.
We have, to calculate the angle measures of

∠ R W E

and

∠ R A E

. It can be observed that these two angles are formed at the intersection of the two unequal sides, so by the property of a kite,

∠ R A E = ∠ R W E

.
Now, according to the angle sum property of a quadrilateral, the sum of all the interior angles of the kite will be

36 0 ∘

.
So, applying this property to the kite WEAR, we get,

∠ R W E + ∠ W E A + ∠ R A E + ∠ A R W = 360 ° ∠ R W E + 70 ∘ + ∠ R W E + 80 ∘ = 360 ∘ 2 ∠ R W E + 150 ∘ = 360 ∘ 2 ∠ R W E = 360 ∘ − 150 ∘ 2 ∠ R W E = 210 ∘ ∠ R W E = 210 ∘ 2 ∠ R W E = 105 ∘

Thus, we have,

∠ R A E = ∠ R W E ∠ R A E = 105 ∘

So, the angle measures of the remaining two angles of the kite WEAR is

105 ∘

each.
Hence, the correct option is (1).

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