In 4TRI, we have TR = TI = 6 and ∠R = 52◦
. Find the measure of ∠T?

Measure of ∠T = 76°

Step-by-step explanation:

From the figure attached,

ΔTRI has two equal sides TR = TI = 6 units

and m∠R = 52°

Since two sides of the triangle are equal therefore, by the property of isosceles triangle, opposite angles of the equal sides will be equal.

m∠R ≅ m∠I = 52°

Since sum of all the interior angles of a triangle = 180°

m∠T + m∠R + m∠I = 180°

m∠T + 52° + 52° = 180°

m∠T = 180 - 104

m∠T = 76°

Therefore, measure of angle T will be 76°.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°