Question

3. If the two angles of a triangle are 45° and 55°, find the third angle. What type of triangle is it?
4. If the vertex angle of an isosceles triangle is 90°, then find the base angles.
5. The angles of a triangle are in the ratio of 2:3:5. Find the angles. What type of triangle is it?
6. Find the measure of each angle of an equilateral triangle.​

Answer 1

Answer:

Third angel = 180°- sum of two angle

=180°- (45°+55°)

= 189°-100°

=80°

Third angel is 80°

4) Sum of two equal angles = 180-90

= 90

As the two angles are same so the base angle = 90/2 = 45

Step-by-step explanation:

i hope it will be very helpful

Answer 2

Solution - 3

$\bf \: \underline{Given} :$ ↴

$\sf \: The \: angle \: of \: \: \triangle \: are \: 45\degree \: and \: 55\degree.$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: We \: have \: to \: find \: \: the \: third \: angle.$

$\sf \: We \: also \: have \: to \: tell \: that \: which \: type \: of \: \triangle \: is \: it.$

$\bf \: As \: we \: know \: that,$

$\boxed{ \pink{\sf \: Sum \: of \: interior \: angle \: of \: a \: \triangle = 180 \degree}}$

$\sf \: Let \: the \: third \: angle \: be \: x.$

$\sf \: Now,$

$\sf \: 45\degree + 55\degree + x = 180\degree$

$\sf \: 100\degree + x = 180\degree$

$\sf \:x = 180\degree - 100\degree$

$\underline{ \red{ \sf \:x = 80\degree }}$

$\sf \: So, \: the \: third \: angle \: of \: the \: triangle \: is \: 80 \degree$

$\underline{ \red{ \sf \: Hence, \: It \: is \: an \: acute \: angled \: triangle.}}$______________________________________

Solution - 4

$\bf \: \underline{Given} :$ ↴

$\sf \: The \: vertex \: angle \: of \: an \: isosceles \: triangle \: is \: 90\degree. \:$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: We \: have \: to \: find \: the \: base \: angle.$

$\bf \: We \: know \: that,$

$\boxed{ \pink{\sf \: Two \: angles \: of \: an \: isosceles \: triangle \: are \: equal. }}$

$\sf \: Let \: the \: base \: base \: angle \: be \: x .$

$\sf \: Then,$

$\sf \: x + x + 90\degree = 180\degree$

$\sf \: 2x + 90\degree = 180\degree$

$\sf \: 2x = 180\degree - 90\degree$

$\sf \: 2x = 90\degree$

$\sf \: x = \dfrac{90}{2}$

$\sf \: x = 45\degree$

$\underline{ \red{ \sf \: Hence \: the \: base \: angle = 45 \degree}}$

______________________________________

Solution - 5

$\bf \: \underline{Given} :$ ↴

$\sf \: The \: angles \: of \: a \: \triangle \: are \: in \: the \: ratio \: of \: 2:3:5.$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: We \: have \: to \: find \: the \: angles.$

$\sf \: We \: also \: have \: to \: tell \: that \: which \: type \: of \: \triangle \: is \: it.$

$\bf \: Let \: us \: assume \: that :$ ↴

$\sf \: Let \: the \: angles \: of \: a \: \triangle \: are \: 2x, \: 3x \: and \: 5x.$

$\bf \: As \: we \: know \: that,$

$\boxed{ \pink{\sf \: Sum \: of \: interior \: angle \: of \: a \: \triangle = 180 \degree}}$

$\sf \: Hence \: \angle A + \angle B + \angle C = 180 \degree.$

$\sf \: 2x + 3x + 5x = 180 \degree$

$\sf \: 10x = 180 \degree$

$\sf \: x = \dfrac{180 }{10}$

$\sf \: x = 18$

$\sf \: Hence,$

$\sf \: First \: angle = 2 \:x \: 18 = \underline{\red{ 36 \degree}}$

$\sf \: Second \: angle = 3 \: x \: 18= \underline{ \red{54 \degree}}$

$\sf \: Third \: angle = 5 \: x \: 18 = \underline{ \red{90 \degree}}$

$\underline{ \red{ \sf \: As \: the\: third \: angle \: is \: 90 \degree, \: so \: it \: a \: right \: angled \: \triangle. }}$

______________________________________

Solution - 6

$\bf \: \underline{To \: find} :$ ↴

$\sf \: We \: have \: to \: find \: the \: measure \: of \: each \: \angle \: of \: an \: equilateral \: \triangle.$

$\sf \: We \: know \: that,$

$\boxed{ \pink{\sf \: In \: equilateral \: \triangle, \: all \: sides \: are \: same. }}$

$\sf \: Then \: each \: angle = \dfrac{180}{3}$

$\sf \: \longrightarrow \: \dfrac{180}{3} \: = \: 60 \degree$

$\underline{ \red{ \sf \: So, \: all \: angles \: are \: of \: 60 \degree. }}$

______________________________________