Answer: 80
Step-by-step explanation:
x.3/2 = 120
x = 120.2/3
x=80
Answer:
50°
Step-by-step explanation:
As usual, the diagram is not drawn to scale.
The chord divides the circle into two arcs that have a sum of 360°. If we let "a" represent the measure of the smaller arc, then we have ...
a + (a+160°) = 360°
2a = 200° . . . . . . . . . . . subtract 160°
a = 100°
The measure of the angle at A is 1/2 the measure of the subtended arc:
acute ∠A = a/2 = (1/2)·100° = 50°
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<em>Comment on this geometry</em>
Consider a different inscribed angle, one with vertex V on the circle and subtending the same short arc subtended by chord AB. Then you know that the angle at V is half the measure of arc AB. This is still true as point V approaches (and becomes) point A on the circle. When V becomes A, segment VA becomes tangent line <em>l</em>, and you have the geometry shown here.
Answer:
E. 35°, 70°
Step-by-step explanation:
Sum of angles add up to 180° in every triangle.
Step 1: Set up equation
a + 2a + 75 = 180
Step 2: Combine like terms
3a + 75 = 180
Step 3: Subtract 75 on both sides
3a = 105
Step 4: Divide both sides by 3
a = 35
So 1 angle is 35°
Step 5: Plug in <em>a</em> to find last angle
2(35) = 70°
Answer:
5.5 yd
Step-by-step explanation:
The angle opposite to x is 20°
Reason: Alternate interior angles are equal
= tan 20°
x = 15 × tan 20° = 5.459553514 yd
That is 5.5 yd (answer rounded off to nearest tenth).
