Question

Which two angles in the triangles below are complementary?

I NEED HELPPPPPPPP

Answer 1

(a) ∠BAC and ∠CAD

Explanation:

You want to know which angles in the figure are complementary.

Complementary angles

Two angles are complementary when the total of their measures is 90°. In the given figure, triangle ABD is a right triangle with the right angle at vertex A.

The two acute angles at vertices B and D will be complementary:

∠ABC and ∠CDA . . . . . not on the list of choices

Ray AC divides the right angle into two complementary parts:

∠BAC and ∠CAD . . . . . first choice on the list

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Additional comment

The two smaller triangles are isosceles. Angles CDA and CAD are both 35°, so have a sum of 70°. Likewise, angles ABC and BAC are both 55°, with a sum of 110°.

Angles BCA and ACD are a linear pair, so have a sum of 180°. They are supplementary, not complementary.

Answer 2

∠ BAC and ∠ CAD

Explanation:

• Complementary angles sum to 90°

∠ BCA and ∠ ACD are a linear pair and sum to 180°

∠ BCA + 110° = 180° ( subtract 110° from both sides )

∠ BCA = 70°

the sum of the 3 angles in a triangle = 180°

in Δ ABC

∠ BAC + 55° + 70° = 180°

∠ BAC + 125° = 180° ( subtract 125° from both sides )

∠ BAC = 55°

in Δ ACD

∠ CAD + 110° + 35° = 180°

∠ CAD + 145° = 180° ( subtract 145° from both sides )

∠ CAD = 35°

then

∠ BAC + ∠ CAD = 55° + 35° = 90°

∠ BAC and ∠ CAD are complementary