Question

is the angles 47°, 72º and 64º form a triangle. Justify your answer.
The vertical angle of an Isoscesles triangle measures (5t-18) and one of the base angles measures
3tº. Find t.​

Answer 1

Answer:

the answer

Step-by-step explanation:

by steps by steps

Answer 2

The angles 47°, 72° and 64° cannot be interior angles of a triangle.

The value of t is 18°.

Given:

• a) Angles 47°, 72º and 64º.
• b) The vertical angle of an Isosceles triangle measures (5t-18)° and one of the base angles measures 3tº.

To find:

• Whether the angles given in a) form a triangle, justify.
• Find the value of t.

Solution:

a) We know that,

The sum of interior angles of a triangle is 180°.

Add the given angles;

${47}^{ \circ} + {72}^{ \circ} + {64}^{ \circ} = {183}^{ \circ}$

It is clear that,

${183}^{ \circ} \neq{180}^{ \circ}$

Thus,

The angles 47°, 72° and 64° cannot be interior angles of a triangle.

b) We know that,

In isosceles triangle two of its sides are equal and angles opposite to equal sides are also equal.

Thus,

Other base angle will be 3t°.

Apply angle sum property of triangle.

$( {5t - 18)}^{ \circ} + {3t}^{ \circ} + {3t}^{ \circ} = {180}^{ \circ}$

${11t}^{ \circ} = {180}^{ \circ} + {18}^{ \circ}$

$t = \frac{198}{11}$

$t = 18^{ \circ}$

Thus,

The value of t is 18°.

Learn more:

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