1. the three angles of a quadrilateral are 55°, 58° and 147° respectively find the four angle
a.80°
b.260°
c.100°
d.10°
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1. the three angles of a quadrilateral are 55°, 58° and 147° respectively find the four angle
a.80°
b.260°
c.100°
d.10°
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Answer:
"Three angles of a quadrilateral are 55°, 58° and 147° respectively. Find the fourth angle."
We know that a quadrilateral has a total sum of 360°, and since our task is to find the missing fourth angle, let us solve for it.
To do this, let A be the first angle, B as the second, C as third, and D as the fourth.
∠A = 55°
∠B = 58°
∠C = 147°
∠D = ?
The sum of these angles must be equal to 360°. So,
∠A + ∠B + ∠C + ∠D = 360°
Next, substitute what was given.
55° + 58° + 147° + ∠D = 360°
Transfer angles from A to C to the other side of the equation.
(Note: When transferring numbers to the other side, we need to change its sign. For instance, when "-8 + 5" is transferred to the opposite side of the equation, it becomes: "8 - 5")
∠D = 360° - 55° - 58° - 147°
To solve this in an easy way, place a parentheses between -55° to -147° like this:
∠D = 360° (-55° - 58° - 147°)
Next, add up the numbers.
∠D = 360° (-113° - 147°)
∠D = 360° - 260°
Subtract.
∠D = 100°
Therefore, we can conclude that the fourth angle measures 100° when the three angles of the quadrilateral are 55°, 58°, and 147°.