Which equation represents this statement?
1 answer:
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m∠1 = 30° (by Vertical angle theorem)
m∠A = 80° (by Triangle sum theorem)
m∠D = 80° (by Triangle sum theorem)
The value of x is 7.5 and y is 9.
Solution:
∠ACB and ∠DCE are vertically opposite angles.
Vertical angle theorem:
<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>
⇒ m∠DCE = m∠ACB
⇒ m∠1 = 30° (by Vertical angle theorem)
In triangle ACD,
Triangle sum property:
<em>Sum of the interior angles of the triangle = 180°</em>
⇒ m∠A + m∠C + m∠B = 180°
⇒ m∠A + 30° + 70° = 180°
⇒ m∠A + 100° = 180°
⇒ m∠A = 100° – 180°
⇒ m∠A = 80° (by Triangle sum theorem)
Similarly, m∠D = 80° (by Triangle sum theorem)
In ΔACD and ΔDCE,
All the angles are congruent, so ΔACD and ΔDCE are similar triangles.
<em>In similar triangle corresponding sides are in the same ratio.</em>
Do cross multiplication.
90 = 12x
7.5 = x
Now, to find y:
Do cross multiplication.
9y = 72
Divide by 9, we get
y = 8
Hence the value of x is 7.5 and y is 9.
Given:
X: The blue marbles.
3X: The red marbles.
A box contains 144 marbles.
SOLVING:
X + 3X = 144
4X = 144
X =
X = 36 ===> The blue marbles.
If there are 3 times as many red marbles as there are blue marbles:
3(36) = 108 ===> The red marbles. SOLUTION
TESTING:
GOOD LUCK...!!!
X: The blue marbles.
3X: The red marbles.
A box contains 144 marbles.
SOLVING:
X + 3X = 144
4X = 144
X =
X = 36 ===> The blue marbles.
If there are 3 times as many red marbles as there are blue marbles:
3(36) = 108 ===> The red marbles. SOLUTION
TESTING:
GOOD LUCK...!!!