Advertisements
Advertisements
प्रश्न
In the given figure, what is z in terms of x and y?
पर्याय
x + y + 180
x + y − 180
180° − (x + y)
x + y + 360°
Advertisements
उत्तर
In the given ΔABC, we need to convert z in terms of x and y
Now, BC is a straight line, so using the property, “angles forming a linear pair are supplementary”
∠ABC + y = 180
∠ABC =180° - y°
Similarly,
∠ACB + x° = 180°
∠ACB = 180° - x
Also, using the property, “vertically opposite angles are equal”, we get,
z = ∠BAC
Further, using angle sum property of the triangle
∠BAC + ∠ABC + ∠ACB = 180°
z° + (180°- y°) + (180° - x°) = 180°
360° + z° - y° - x° = 180°
180° + z° = y° + x°
z° = y°+ x° -180°
Thus, z = y + x -180°
APPEARS IN
संबंधित प्रश्न
In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
Find the measure of each exterior angle of an equilateral triangle.
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Which of the following statements are true (T) and which are false (F) :
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
In ΔABC, side AB is produced to D so that BD = BC. If ∠B = 60° and ∠A = 70°, prove that: (i) AD > CD (ii) AD > AC
In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC
Which of the following statements are true (T) and which are false (F)?
Sum of the three sides of a triangle is less than the sum of its three altitudes.
Fill in the blank to make the following statement true.
The sum of three altitudes of a triangle is ..... than its perimeter.
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
If the angles A, B and C of ΔABC satisfy the relation B − A = C − B, then find the measure of ∠B.
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
In the given figure, what is y in terms of x?
In the given figure, the value of x is ______.
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
Find all the angles of an equilateral triangle.
