Question

find the unknown marked angles in each of the following figures​

Answer 1

Answer:

X = 135° (exterior angle)

X = 45° ( interior angle)

Step-by-step explanation:

Here if you observe carefully two sides of the triangle are equal.

This means that this is a isosceles right angle triangle.

So in a right angled isosceles triangle one angle = 90°

Other two angles = 45°

Here they are asking one exterior angle and one interior angle.

Now to get exterior angle X

Interior angle is equal to 45°

So exterior angle will be :-

180 - 45 = 135°

Exterior angle will be 135°

Interior angle = 45°

This is because it is an right angled isosceles triangle.

Answer 2

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In Triangle ABC

Given measure of Angle C = 90°

[Sum of all angles of Triangle = 180°]

Given that Angle A = Angle C (Isosceles Triangle)

Let measure of Angle A be x

Angle A = Angle C = x

x + x + 90 = 180

2x + 90 = 180

2x = 180 - 90

2x = 90

x = 90/2

x = 45°

Thus,

Angle A = 45°

Angle B = 90°

Angle C = 45°

Now Angle D

Given Angle D = x

x + 45° (Angle A) = 180° [Linear Pair]

x = 180° - 45°

x = 135°

Angle D = 135°