Maths-
General
Easy

Question

ABC is an equilateral triangle. Base BC is produced to E. Such that BC= CE. Calculate straight angle A C E text  and  end text straight angle A E C?

hintHint:

Use the property of isosceles triangle.

The correct answer is: 30°




    ΔABC, is an equilateral triangle.
    straight angle A B C equals straight angle C B A equals straight angle A C E equals 60 to the power of ring operator
    Sum of 2 non adjacent interior angles of a triangle is equal to the exterior angle
    not stretchy rightwards double arrow straight angle C A B plus straight angle C B A equals straight angle A C E
    not stretchy rightwards double arrow 60 to the power of ring operator plus 60 to the power of ring operator equals straight angle A C E
    not stretchy rightwards double arrow straight angle A C E equals 120 to the power of ring operator
    Now, ΔACE is an isosceles triangle with AC = CE
    not stretchy rightwards double arrow straight angle E A C equals straight angle A E C
    Sum of all angles of a triangle is 1800
    not stretchy rightwards double arrow straight angle E A C plus straight angle A E C plus straight angle A C E equals 180 to the power of ring operator
    not stretchy rightwards double arrow 2 straight angle A E C plus 120 to the power of ring operator equals 180 to the power of ring operator
    not stretchy rightwards double arrow 2 straight angle A E C equals 180 to the power of ring operator minus 120 to the power of ring operator
    not stretchy rightwards double arrow 2 straight angle A E C equals 60 to the power of ring operator
    not stretchy rightwards double arrow straight angle A E C equals 30 to the power of ring operator

    Related Questions to study

    General
    Maths-

    Find the smallest number by which 694 should be multiplies , so that product is a perfect square.

    Find the smallest number by which 694 should be multiplies , so that product is a perfect square.

    Maths-General
    General
    Maths-

    The perpendicular bisectors of the sides of a triangle ABC meet at point I. prove that IA=IB=IC

    The perpendicular bisectors of the sides of a triangle ABC meet at point I. prove that IA=IB=IC

    Maths-General
    General
    Maths-

    Use prime factorization method to find the square root of each of the following :
    c) 1089

    Use prime factorization method to find the square root of each of the following :
    c) 1089

    Maths-General
    parallel
    General
    Maths-

    Use prime factorization method to find the square root of each of the following :
    b)175

    Use prime factorization method to find the square root of each of the following :
    b)175

    Maths-General
    General
    Maths-

    Use prime factorization method to find the square root of each of the following :
    a)11025

    Use prime factorization method to find the square root of each of the following :
    a)11025

    Maths-General
    General
    Maths-

    In Triangle ABC , AB= AC, and D is a point on AB. Such that AD=DC=BC. Show that straight angle B A C equals 36 to the power of ring operator

    In Triangle ABC , AB= AC, and D is a point on AB. Such that AD=DC=BC. Show that straight angle B A C equals 36 to the power of ring operator

    Maths-General
    parallel
    General
    Maths-

    In the triangle ABC, the angles at A and C are 40° and 95° respectively. If N is the foot of the perpendicular from C to AB , prove that CN = BN.

    In the triangle ABC, the angles at A and C are 40° and 95° respectively. If N is the foot of the perpendicular from C to AB , prove that CN = BN.

    Maths-General
    General
    Maths-

    Given XYZ is a triangle in which XW is the bisector of the angle x and XW ⊥ yz. Prove that xy= xz.

    Given XYZ is a triangle in which XW is the bisector of the angle x and XW ⊥ yz. Prove that xy= xz.

    Maths-General
    General
    Maths-

    ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively are equal. Show that
    (i) ΔABE ⩭ ΔACF
    (ii)  AB = AC

    ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively are equal. Show that
    (i) ΔABE ⩭ ΔACF
    (ii)  AB = AC

    Maths-General
    parallel
    General
    Maths-

    In the figure, OA = OD and OB = OC. Show that:
    (i) AOB ⩭ DOC
    (ii)  AB || CD

    In the figure, OA = OD and OB = OC. Show that:
    (i) AOB ⩭ DOC
    (ii)  AB || CD

    Maths-General
    General
    Maths-

    If AD ⟂ CD and BC ⟂ CD , AQ = PB and DP = CQ. Prove that straight angle D A Q equals straight angle C B P

    If AD ⟂ CD and BC ⟂ CD , AQ = PB and DP = CQ. Prove that straight angle D A Q equals straight angle C B P

    Maths-General
    General
    Maths-

    Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:
    (i) AOD ⩭ BOC
    (ii)  AD || BC

    Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:
    (i) AOD ⩭ BOC
    (ii)  AD || BC

    Maths-General
    parallel
    General
    Maths-

    Kumar wants to spread a carpet on the floor of his classroom. The floor is a square
    with an area of 4160.25 square feet. What is the length of carpet on each side?

    Kumar wants to spread a carpet on the floor of his classroom. The floor is a square
    with an area of 4160.25 square feet. What is the length of carpet on each side?

    Maths-General
    General
    Maths-

    The volume of a cubical box is 12167 cm3. Find the side of the box and its 6 sides area?

    The volume of a cubical box is 12167 cm3. Find the side of the box and its 6 sides area?

    Maths-General
    General
    Maths-

    The area of a square is 289 m2, find its perimeter?

    The area of a square is 289 m2, find its perimeter?

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.