Question

If ∠adb = 70°, then match the following to their values. hint: since bd is a diameter, you can find the measure of angle dab using theorem 6-10. 1. m = 20 2. m∠abd = 40 3. m = 140

Answer 1

To find the value of angle DAB, you can use Theorem 6-10, which states that the measure of angle formed by a chord and a tangent at the point of contact is half the measure of the intercepted arc. Given that angle ADB = 70°, you can find angle DAB by dividing the intercepted arc AB by 2.

Step-by-step explanation:

To find the value of angle DAB, we can use Theorem 6-10, which states that the measure of angle formed by a chord and a tangent at the point of contact is half the measure of the intercepted arc.

Since BD is a diameter, angle DAB is formed by chord AD and tangent BD at point D. The intercepted arc is arc AB.

Given that angle ADB = 70°, we can use the theorem to find angle DAB. Since arc AB = 2 * angle ADB (theorem 6-10), arc AB = 2 * 70° = 140°. Therefore, angle DAB = 140° / 2 = 70°.

Therefore, angle DAB has a measure of 70°, matching option 3. m∠abd = 40 is incorrect because it is the measure of angle ABD, not angle DAB.