In the circle below, ∡DAB and ∡DCB are right angles and m∡BDC = 29°. The figure is not drawn to scale.
Image: www(dot)connexus(dot)com/content/media/941080-7222013-25617-PM-1443351303(dot)gif
What is m CAD
a. 156°
b. 204°
c. 238°
d. 282°
We know that angles ∡DAB and ∡DCB are right angles, so they each measure 90°. Since the sum of the angles in a triangle is 180°, we can find m∡CBD by subtracting 90° and 29° from 180°:
m∡CBD = 180° - 90° - 29° = 61°
Since angles ∡CAB and ∡CBD are supplementary (their sum is 180°), we can find m∡CAB by subtracting 61° from 180°:
m∡CAB = 180° - 61° = 119°
Finally, since angles ∡CAD and ∡CAB are complementary (their sum is 90°), we can find m∡CAD by subtracting 119° from 90°:
m∡CAD = 90° - 119° = -29°
However, we cannot have a negative angle measure, so we need to add 360° to get an angle in standard position:
m∡CAD = -29° + 360° = 331°
Therefore, the answer is not one of the given options.
To find the measure of angle CAD, we need to consider the properties of angles in a circle.
In a circle, the sum of the measures of angles formed by intersecting chords, secants, or tangents is equal to 360°.
In this case, we have a right angle ∡DAB and a right angle ∡DCB, which means they both measure 90°.
Since the sum of the measures of all the angles in a circle is 360°, we can calculate the measure of angle CAD.
360° - 90° - 90° - 29° = 151°
Therefore, the measure of angle CAD is 151°.
None of the answer choices provided match the calculated measure, so the correct answer is not given.