Question

please give me answer

Answer 1

Answer:

Given :-

• In the given figure, ∠ABC = 44°, ∠BAC = 30° & ∠EDC = 48°.

To find :-

• Values of x and y.

Property used :-

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Solution:-

In ∆ ABC,

Using exterior angle property of triangle,

$\bf\implies \:∠BAC + ∠ABC = y$

$\bf\implies \:30° + 44° = y$

$\bf\implies \:y = 74°$

Now, In ∆EDC,

Using exterior angle property of triangle,

$\bf\implies \:∠EDC + y = x$

$\bf\implies \:48° + 74° = x$

$\bf\implies \:x = 122°$

$\bf\implies \:values \: of \: x \: and \: y \: are \: 122° \: and \: 74°$

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Additional Information

Properties of a triangle

• A triangle has three sides, three angles, and three vertices.

• The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• The side opposite to the largest angle of a triangle is the largest side.

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Based on the angle measurement, there are three types of triangles:

• Acute Angled Triangle : A triangle that has all three angles less than 90° is an acute angle triangle.

• Right-Angled Triangle : A triangle that has one angle that measures exactly 90° is a right-angle triangle.

• Obtuse Angled Triangle : triangle that has one angle that measures more than 90° is an obtuse angle triangle.