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The sum of exterior angles of a convex pentagon, hexagon, and heptagon are respectively:
The sum of exterior angles of any convex polygon is 360°. 360° = 4 * 90° = 4 right angles.
In the following, the value of is-
The exterior angle of a triangle is equal to the sum of opposite interior angles. .
Find the value of x in the given figure
Angle subtended by an arc at the circumference is half the angle subtended at the center. Hence 100°/2 = 50°.
In the given figure, lines AB and CD intersect at point O. If OE and OF are the bisectors of ∠BOD and ∠COB respectively and if ∠EOD = 25°, then ∠COF is equal to-
∠BOD = 2 * 25° = 50°. From linear pair, ∠COB = 180° - 50° = 130°. Thus, ∠COF = 1/2 * ∠COB = 130/2 = 65°.
If a transversal intersects two parallel lines, then each pair of corresponding angles is-
According to the property of parallel lines, each pair of corresponding angles is equal.
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The angle formed between the internal bisector of angle B and the external bisector of angle C on the base BC of a triangle ABC will be equal to which of the following angles? [RPSC LDC-17.02.2012]
Geometry theorem: The angle formed by the internal bisector of one angle and the external bisector of another angle is half the third angle. Here, ∠BEC = 1/2 ∠A.
If ΔABC ≅ ΔFDE and AB = 5 cm, ∠B=40° and ∠A=80°, which of the following is correct? [REET(L-II), 26.09.2021]
ΔABC ≅ ΔFDE. So corresponding parts are equal. AB = FD = 5. ∠A = ∠F = 80°. ∠B = ∠D = 40°. ∠C = ∠E = 180° - (80°+40°) = 60°. Hence DE = AB = 5 cm, ∠E = 60°.
Two straight lines AB and CD intersect each other at point O. If ∠AOC = 50°, then ∠BOC = ?
∠AOC + ∠BOC = 180° (Linear pair). 50° + ∠BOC = 180° => ∠BOC = 130°.
The measure of an angle whose supplementary angle measure is equal to four times its complementary angle measure is-
Let the angle be θ. According to the question: (180 - θ) = 4 * (90 - θ) => 180 - θ = 360 - 4θ => 3θ = 180 => θ = 60°.
In the given figure, AOB is a straight line on which ray OC is incident. If , then what will be the value of ?
Sum of ratios = . Total angle on line AOB = 180°. Therefore, angle .
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What will be the value of x in the given figure? [VDO Main's-09.07.2022]
ΔPNK ~ ΔLMK (AA similarity). Corresponding sides will be proportional: PN/LM = NK/MK => x/a = c/(b+c) => x = ac/(b+c).
Construction of the following angle is not possible with the help of a ruler and compass-
Construction of 39.5° is not possible with compass and ruler because it is not a multiple of 3.75°.
The sum of all interior angles of a pentagon is-
Formula (n-2) * 180°. For a pentagon n=5, so (5-2) * 180° = 3 * 180° = 540°.
If a transversal line intersects two parallel lines, which of the following statements is NOT true regarding the angles formed?
The sum of interior angles on the same side of a transversal is 180° (two right angles). Option (D) is incorrect as it states 90°.
The four angles of a rectangle are-
All four angles of a rectangle are 90° (right angles).
A tangent PQ at point P to a circle of radius 5 cm meets a line through center O at point Q such that OQ=12 cm. The length of PQ will be- [VDO Main's-09.07.2022]
Triangle OPQ is a right-angled triangle where ∠P = 90°. PQ = √(OQ² - OP²) = √(12² - 5²) = √(144 - 25) = √119 cm.
If a transversal line intersects three parallel straight lines, what will be the number of different values of the angles formed?
When a transversal intersects parallel lines, only two types of angles are formed (one acute and one obtuse), which are supplementary to each other.
The point equidistant from the three vertices of a triangle is called-
The Circumcenter is the point that is equidistant from the three vertices of a triangle.
In the given figure, OP || RS, ∠OPQ = 100° and ∠QRS = 140°, then ∠PQR will be equal to-
Draw a line through Q parallel to OP and RS. Using the property of alternate interior angles, calculating gives ∠PQR = 60°.
The number of lines of symmetry for a regular hexagon is-
A regular hexagon has 6 lines of symmetry.
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Mathematics
