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A line \( AB \) intersects the line \( PQ \) at \( K \). If the \( \angle PKA = \angle PKB \), what is the measure of the angle \( \angle PKA \)?
because the angle on a straight line is 180°.
(1)
Find the value of \( k \) in the following figure.
Sum of all angles is equal to 180° because the angle on a straight line is 180°.
(1)
The angles of a triangle are \( k15^{\circ}, 2k+45^{\circ} \) and \( k10^{\circ} \). Find the measure of the smallest angle.
Sum of all angles of a triangle is equal to 180°.
(1)
Smallest angle of the triangle is 40° – 15° = 25°.
Find the measure of the angle \( k \) in the following figure.
and Sum of all angles of a triangle is equal to 180°.
(1)
The ratio of two complementary angles is \( 3:5 \). Find the larger angle.
If two angles are complementary then their sum is 90°.
(1)
Larger angle is 5 times 11.25° that is 56.25°.
The ratio of three supplementary angles is \( 3:5:10 \). Find the largest angle.
If three angles are supplementary then their sum is 180°.
(1)
Largest angle is 10 times 10° that is 100°.
If \( m = 3n = 6p \) in the following figure, find the value of \( m \).
From the given ration, we can write and
(1)
Therefore, .
Lines \( PQ, RS \) and \( TU \) are parallel to each other. Lines \( AB \) and \( CD \) are also parallel to each other in the following figure. Find the value of \( \angle ABC \).
and
(1)
Therefore,
(2)
Exterior angle of a triangle is \( 126^{\circ} \) and one of the opposite interior angle is \( 42^{\circ} \). Find the other two angles.
We know that the exterior angle of a triangle is equal to the sum of two opposite interior angles. Let the second interior angle be .
(1)
Let the third angle of the triangle be . Therefore,
(2)
The measure of an angle is 8 times the measure of its supplement. Find the angles.
(1)
If two complementary angles are in the ratio 5:4, then find the angles.
(1)
In the following figure, find the value of y.
(1)
P, Q and R are the three angles of a triangle. If PQ = 20° and QR = 26°, then find the value of angle Q.
(1)
In the following figure, line AB is parallel to CD. Find the value of angle BOC.
Draw a line PQ parallel to AB and CD
(1)
In the following figure, line QR is parallel to ST. Find the value of y.
(1)
Two straight line MN and PQ intersect each other at point O. If \( \angle MOP + \angle MOQ + \angle NOP = 285^{\circ} \), find the value of \( \angle NOQ \)
(1)
In a triangle PQR, \( \angle P = 50^{\circ} and \angle Q = 77^{\circ} \). Find the shortest and largest side respectively.
RQ is shortest (side opposite to smallest angle is shortest) and PR is longest (side opposite to biggest angle is largest)
In the given figure, line AB is parallel to CD. Find the value of angle NMO.
(1)
If in a triangle, angles are in the ratio 1:4:7, then find the largest angle.
(1)