In the diagram, m CD = 128° and m DA = 76°. What is m∠ABC?

2 answers:

7 0

Angle ABC is an inscribed angle.

Inscribed angle = 1/2 * Intercepted Arc

The intercepted arc is arc CD + arc DA, which would be 128 + 76 = 204

m<ABC = 1/2(204)

m<ABC = 102 degrees

You answer is D) 102

Vikki [24]4 years ago

6 0

Answer: The value of m∠ABC is 102° .

Step-by-step explanation:

Since we have given that

m CD = 128°

m DA = 76°

We need to find the m∠ABC, Angle subtended at the center is half of the sum of the measure of the arc intercepted by it.

$\frac{m\ CD+m\ DA}{2}=\angle ABC\\\\\frac{128^\circ+76^\circ}{2}=\angle ABC\\\\102^\circ=m\angle ABC$

The value of m∠ABC is 102° .

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In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AH=4 and HC=1, find BH.

faltersainse [42]

Answer:

$BH=2$

Step-by-step explanation:

Please find the attachment.

We have been given that triangle ABC is a right triangle, having a right angle at point B and BH is the altitude.

We can see from our attachment that the altitude BH is drawn to hypotenuse AC.

Altitude geometric mean theorem states that the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. Each leg of the right triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

Using the above theorem we can set proportions for our given side lengths as:

$\frac{\text{Left}}{\text{Altitude}}=\frac{\text{Altitude}}{\text{Right}}$